The product of 2 2 matrices A and B is the matrix AB defined by The

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The product of 2 × 2 matrices A and B is the matrix AB defined by

a b b' ( 5 ) ( 25 ) = C d A B aa' + bc ca' + de' ab' + bd' cb' + dd' AB

The (i, j)-entry of A is the dot product of the ith row of A and the jth column of B. Prove that det(AB) = det(A) det(B).

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Jan 23, 2024 12:01 PM

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The product of 2 2 matrices A and B is the matrix AB defined by The

Question:

a b b' ( 5 ) ( 25 ) = C d d' A B aa' + bc' ca' + de' ab' + bd' cb' + dd' AB

Step by Step Answer:

The determinants of A and B are detAB detA We combine 1 and 2 to con...View the full answer

Calculus

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