# Proving some identities of invertble matrices

Can you help me prove the following:

If A is an invertible matrix and n is a non negative integer then:

a) A^-1 is invertible and (A^-1)^-1 = A

b) A^n is invertible and (A^n)^-1 = A^-n = (A^-1)^n

Please show all work in detail

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#### Solution Preview

The proofs are on the file: Algebra.doc

Prove the following:

If A is an invertible matrix and n is a non negative integer then:

a) A^-1 is invertible and (A^-1)^-1 = A

Proof. As A is invertible, if we denote its inverse by , then

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#### Solution Summary

This solution consists of detailed proofs of the following statements:

If A is an invertible matrix and n is a non negative integer, then

a) A^-1 is invertible and (A^-1)^-1 = A

b) A^n is invertible and (A^n)^-1 = A^-n = (A^-1)^n