(i) Use the definition of inverse to prove the following: if A and B are n ...

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(i) Use the definition of inverse to prove the following: if A and B are n × n nonsingular matrices, then (AB)-1 = B-1A-1.

(ii) If A, B, and C are all n × n nonsingular matrices, find (ABC2)-1 in terms of A-1, B-1, and C-1.

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