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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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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.`
Posted by sciencesolve on April 26, 2013 at 2:35 PM (Answer #1)
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