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## Homework Statement

Suppose that ##A^2 = 0##. Show that ##A## is not an invertible matrix

## Homework Equations

## The Attempt at a Solution

We can do a proof by contradiction. Assume that ##A^2 = 0## and that ##A## is invertible. This would imply that ##A=0##, which is to say that A is not invertible, since ##0## has no inverse. This is a contraction, so it must be the case that if ##A^2 = 0##, then ##A## is not invertible.

Is this the way I should be doing this problem?