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## Homework Statement

I'm attempting to prove a property of inverse matrices. The property is as follows:

(A

^{k})

^{-1}= (A

^{-1})

^{k}

## Homework Equations

A

^{-1}A = I

## The Attempt at a Solution

(A

^{-1})

^{k}= A

^{-1}A

^{-1}....A

^{-1}= (A

^{k})

^{-1}

I postulated that you could factor a k based on A

^{-1}being multiplied k number of times.

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