Why is that Nullspace of A is subset of nullspace of A^T*A

[iamzzz]

Why is that Nullspace of A is subset of nullspace of A^T*A
let's say that A is m*n matrix

 

[lurflurf]

Suppose
X is the null space of A
AX=0
then clearly
A^T*AX=A^T0=0
X may not be the whole null space of A^T

 

[iamzzz]

Thanks