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## Homework Statement

For any (nxn) matrix A, prove or disprove with a counter example:

1. Rank(A^2) <= rank(A)

2. Nullity(A^2) <= nullity(A)

## Homework Equations

Rank = dimension of range

Nullity = dimension of null space

## The Attempt at a Solution

I have been trying a few examples with both nonsingular and singular matrices and in all the cases I have found that rank(a^2) = rank(a) and like wise for the nullity. But obviously isn't enough to convince me so I was looking for some help please.