Proving Singular Matrix A Has Nonzero Matrix B: Linear Algebra Problem

[Braka]

The problem is prove that for every square singular matrix A there is a nonzero square matrix B, such that AB equals the zero matrix.

I got AB to equal the identity matrix, but not the zero matrix.

 

[Mystic998]

Yeah, that would be bad, because that would imply that A is nonsingular. Anyway, think about what singularity implies for the columns of A.