## Rank and Nullity of a Matrix, Nullity of Transpose

## Problem 140

Let $A$ be an $m\times n$ matrix. The nullspace of $A$ is denoted by $\calN(A)$.

The dimension of the nullspace of $A$ is called the nullity of $A$.

Prove the followings.

**(a)** $\calN(A)=\calN(A^{\trans}A)$.

**(b)** $\rk(A)=\rk(A^{\trans}A)$.