Determining invertible matrix

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Reference no: EM13131934

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 make the proof very detailed and show every step

Reference no: EM13131934

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