Question: The following statements are needed to prove Theorem 6.12. a. Show that if A1 exists, it is unique. b. Show that if A is nonsingular,

The following statements are needed to prove Theorem 6.12.
a. Show that if A−1 exists, it is unique.
b. Show that if A is nonsingular, then (A−1)−1 = A.
c. Show that if A and B are nonsingular n×n matrices, then (AB)−1 = B−1A−1.

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