# Rank of a matrix

1. Jan 30, 2010

### katyyara

Hi,

Does anyone know how to prove rank(A)=rank(AT A) where A is any matrix and AT is the transposed of matrix A? I have difficulty to prove the part that nulity(A)=nulity(AT A). Any help will be appreciated.

2. Jan 30, 2010

### rochfor1

Try proving $$\operatorname{ker} A = \operatorname{ker} ( A^\top A)$$.