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## Homework Statement

Show that the square matrix [tex]2N - I[/tex] is its own inverse if [tex]N^{2} = N[/tex]

## Homework Equations

properties of invertible matrix

## The Attempt at a Solution

I really don't know where to start here. I know that [tex](2N-I)(2N-I) = I[/tex], but where do I go on from there?