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    1) if A, B are square and AB=I_n, then det B=1/det A
    2) if A, B, S are square and B=(S^-1)AS, then det B=det A
    3) If A is square and (A^T)A=I_n, then det A= +/- 1
    4) if A is n x n and A^T= -A, then det A= (-1)^n det A. In particular, if n is odd, then det A=0

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    Solution Summary

    The expert provides proofs about determinants.