a) Find the determinants of the following matrices. and b) Find det(AB), det(A–1), and det...

a) Find the determinants of the following matrices.

 and

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b) Find det(AB), det(A–1), and det(BTA–1) without finding AB, A–1, or BTA–1.

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c) Show that det(A + B) is not the same as det(A) + det(B).