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## Homework Statement

Show that if A ε M

_{nxn}is nonsingular and t ≠ 0, then tA is nonsingular and

(tA)

^{-1}= (1/t)A

^{-1}.

## Homework Equations

## The Attempt at a Solution

I need to show an intense proof of this statement. Although I can grasp the concept in my head, I am unsure as to the mathematical reasons and theorems that prove this true.