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5. (a) Prove that det(AAT ) = (det(A))2. (b) Suppose that A is an n×n matrix...

5. (a) Prove that det(AAT ) = (det(A))2.
(b) Suppose that A is an n×n matrix such that AT = −A. (Such an A is called a skew- symmetric matrix.) If n is odd, prove that det(A) = 0.

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