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If A and B are 4x4 matrices, det(A) = -4 , det(B) = 3, then det(AB) = ?

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goldbergfan | Student | (Level 2) Honors

Posted April 26, 2013 at 2:18 PM via web

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If A and B are 4x4 matrices, det(A) = -4 , det(B) = 3, then det(AB) = ?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 26, 2013 at 2:30 PM (Answer #1)

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You need to use one of properties of determinants, hence, since the matrices A and B are square matrices of same size, you should consider the following properties, such that:

`det(A*B) = det A*det B`

Since the problem provides the information `det A = -4` , `det B = ` 3, hence, you may evaluate `det(A*B)` replacing -4 for det A and 3 for det B, such that:

`det(A*B) = -4*3 => det(A*B) = -12`

Hence, evaluating det(A*B), using one of properties of determinants, yields `det(A*B) = -12.`

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