a) If A and B are invertible and their inverses are A¹ and B-¹ respectively, prove that the inverse of AB is B-¹A-¹. b) Let A and B be square matrices, with A being invertible. If you know that C = AB is also invertible, find an expression for A involves B and C-1 c) Let A be a square matrix. Suppose that for some nonzero vector , we have Ax=0. Prove that A is not invertible. d) Let A be a square matrix. Let B be the inverse of A2. Show that AB is the inverse of A. that

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