https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:matrices/e/multiplying_a_matrix_by_a_matrix 2026-03-25T08:45:54.138212971Z आव्यूह का गुणन (Multiply matrices)। दिए गए दो आव्यूहों का गुणनफल ज्ञात कीजिए। Tomer Gal exercise https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:matrices-ncert-new/x7ce8ca9c5869750b:multiplication-by-a-matrix/v/commutative-property-matrix-multiplication 2021-03-25T01:54:36Z क्या आव्यूहों का गुणन क्रम विनिमेय है? Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way). Sal Khan video https://cdn.kastatic.org/googleusercontent/WJR2HLZMFiOH6UEMJBxbFA4kAksb7KVyEteoWXm-tMbL6IcnVzmHPrqowjX9sAbnMyXzfCYgo6Otx8iq86bwVWcB क्या आव्यूहों का गुणन क्रम विनिमेय है? Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way). https://cdn.kastatic.org/ka-youtube-converted/xVRNGj1pxSQ.mp4/xVRNGj1pxSQ.mp4 452 आव्यूह से गुणनफल https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:matrices-ncert-new/x7ce8ca9c5869750b:multiplication-by-a-matrix/v/associative-property-matrix-multiplication 2021-03-25T01:54:36Z आव्यूहों के गुणन का साहचर्य गुणधर्म Sal shows that matrix multiplication is associative. Mathematically, this means that for any three matrices A, B, and C, (A*B)*C=A*(B*C). Sal Khan video https://cdn.kastatic.org/googleusercontent/pmLLh5x1lgfZvgSJ0tcBps-WRAbPR55vRtP3I4cnQwijpNXwTR8pHIYvToKJNfJo1hRFLxbWThRSnO4U7J5jc-I आव्यूहों के गुणन का साहचर्य गुणधर्म Sal shows that matrix multiplication is associative. Mathematically, this means that for any three matrices A, B, and C, (A*B)*C=A*(B*C). https://cdn.kastatic.org/ka-youtube-converted/lMIG-pWyMNM.mp4/lMIG-pWyMNM.mp4 517 आव्यूह से गुणनफल https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:matrices-ncert-new/x7ce8ca9c5869750b:multiplication-by-a-matrix/v/distributive-property-of-matrix-multiplication 2025-06-25T04:37:22.958747522Z आव्यूहों के गुणन का वितरण नियम In this video, we verify distributive property of multiplication of matrices. Just like scalars, we can mutliply matrices using distributive properties. We first look at a scenario where we have 3x3 matrices. We then pick a scenario where we have 2x2 matrices. Finally, we also observe that A(B+C) is not the same as (B+C)A. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw आव्यूहों के गुणन का वितरण नियम In this video, we verify distributive property of multiplication of matrices. Just like scalars, we can mutliply matrices using distributive properties. We first look at a scenario where we have 3x3 matrices. We then pick a scenario where we have 2x2 matrices. Finally, we also observe that A(B+C) is not the same as (B+C)A. https://cdn.kastatic.org/ka-youtube-converted/eKYvFK4CqgI.mp4/eKYvFK4CqgI.mp4 495 आव्यूह से गुणनफल https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:matrices-ncert-new/x7ce8ca9c5869750b:multiplication-by-a-matrix/v/zero-matrix 2021-03-25T01:54:36Z शून्य आव्यूह और आव्यूहों का गुणन Just as any number multiplied by zero is zero, there is a zero matrix such that any matrix multiplied by it results in that zero matrix. Learn more from Sal. Sal Khan video https://cdn.kastatic.org/googleusercontent/i-6W_dqrs-9neFNYpv9PGKBR95MhQqjDY_uKtketTzFi90_TAT9tLgs5G3QHPMrhu4nAMhqKjXNS3Zs18ewF7eyQog शून्य आव्यूह और आव्यूहों का गुणन Just as any number multiplied by zero is zero, there is a zero matrix such that any matrix multiplied by it results in that zero matrix. Learn more from Sal. https://cdn.kastatic.org/ka-youtube-converted/NRauugGvxuo.mp4/NRauugGvxuo.mp4 282 आव्यूह से गुणनफल https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:matrices-ncert-new/x7ce8ca9c5869750b:multiplication-by-a-matrix/v/evaluating-expressions-using-matrix-multiplication 2025-06-25T04:37:22.958747522Z आव्यूहों के गुणन का उपयोग करके व्यंजकों को हल करना In this video, we learn how to evaluate expressions when a square matrix is given. We first evaluate a quadratic expression using a 2x2 matrix. We then evaluate a cubic expression using a 3x3 matrix. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw आव्यूहों के गुणन का उपयोग करके व्यंजकों को हल करना In this video, we learn how to evaluate expressions when a square matrix is given. We first evaluate a quadratic expression using a 2x2 matrix. We then evaluate a cubic expression using a 3x3 matrix. https://cdn.kastatic.org/ka-youtube-converted/BY9gZcKZ8g4.mp4/BY9gZcKZ8g4.mp4 463 आव्यूह से गुणनफल https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:matrices-ncert-new/x7ce8ca9c5869750b:multiplication-by-a-matrix/v/applying-trigonometric-identities-to-evaluate-matrices 2025-06-25T04:37:22.958747522Z त्रिकोणमितीय सर्वसमिकाओं का उपयोग करके आव्यूहों को हल करना In this video, we learn how to apply trigonometric identities to evaluate sums and products of matrices. In addition to matrix addition and multiplication properties, we also apply our knowledge from the trigonometry unit to solve these problems. For the problems covered in this video, we appy Pythagorean identity, angle sum property, and half angle identiy. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw त्रिकोणमितीय सर्वसमिकाओं का उपयोग करके आव्यूहों को हल करना In this video, we learn how to apply trigonometric identities to evaluate sums and products of matrices. In addition to matrix addition and multiplication properties, we also apply our knowledge from the trigonometry unit to solve these problems. For the problems covered in this video, we appy Pythagorean identity, angle sum property, and half angle identiy. https://cdn.kastatic.org/ka-youtube-converted/2hspMNEdzq8.mp4/2hspMNEdzq8.mp4 516 आव्यूह से गुणनफल https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-1/x6a634f0b79812b7f:matrices/v/solving-for-matrix-given-product 2025-06-25T04:37:22.958747522Z दिए हुए गुणनफल से आव्यूह ज्ञात करना In this video, we learn how to find one of the matrices if we know the other one and their product. To find a 2x2 matrix, we need to solve 4 equations (for 4 variables). We solve 2 problems in this video. For the second one, we first try to find the order of the missing matrix before solving for its elements. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw दिए हुए गुणनफल से आव्यूह ज्ञात करना In this video, we learn how to find one of the matrices if we know the other one and their product. To find a 2x2 matrix, we need to solve 4 equations (for 4 variables). We solve 2 problems in this video. For the second one, we first try to find the order of the missing matrix before solving for its elements. https://cdn.kastatic.org/ka-youtube-converted/O1BYGoq15OA.mp4/O1BYGoq15OA.mp4 563 आव्यूह से गुणनफल https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:matrices-ncert-new/x7ce8ca9c5869750b:multiplication-by-a-matrix/v/conceptual-problems-on-multiplication-of-matrices 2025-06-25T04:37:22.958747522Z आव्यूहों के गुणन से जुड़े अवधारणात्मक प्रश्न In this video, we solve a conceptual problem that tests our understanding of properties of addition and multiplication of matrices. We try to figure out the restrictions on the number of rows and columns of the given matrix provided that the given expression is defined. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw आव्यूहों के गुणन से जुड़े अवधारणात्मक प्रश्न In this video, we solve a conceptual problem that tests our understanding of properties of addition and multiplication of matrices. We try to figure out the restrictions on the number of rows and columns of the given matrix provided that the given expression is defined. https://cdn.kastatic.org/ka-youtube-converted/mOQZzWNu48w.mp4/mOQZzWNu48w.mp4 339 आव्यूह से गुणनफल