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If A and B are 4x4 matrices, det(A) = -4 , det(B) = 3, then det(B^2) = ?

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chocobob | Student | Honors

Posted April 26, 2013 at 2:19 PM via web

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If A and B are 4x4 matrices, det(A) = -4 , det(B) = 3, then det(B^2) = ?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 26, 2013 at 2:35 PM (Answer #1)

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You need to use the following property of determinants of square matrices of same size, such that:

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

Reasoning by analogy, yields:

`det(B^2) = det(B*B) = det B*det B = (detB)^2`

Since the problem provides `det B = 3` , you need to replace 3 for `det B` in equation above, such that:

`det(B^2) = 3*3 => det(B^2) = 9`

Hence, evaluating `det(B^2) = 9` , using the property of square matrices of same size, yields `det(B^2) = 9.`

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