Consider the following theorem. Properties of Inverse Matrices If A is an invertible matrix, k is a positive integer, and c is a nonzero scalar, then A-1, Ak, CA, and AT are invertible and the statements below are true. 1. (A-1)-1 = A 2. (Ak)-1 = A-A-1...A-1 = (A-1)k k factors 3. (CA)-1 = LA-1 4. (AT)-1 = (A-1)T Prove Property 4 of the above theorem. If A is an invertible matrix, then (AT)-1 = (A-1)7.

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