# Square Matrix with Duplicate Columns has Zero Determinant/Corollary

## Corollary to Square Matrix with Duplicate Columns has Zero Determinant

If a square matrix has a zero column, its determinant is zero.

## Proof

If you add any column to a zero column, you get a square matrix with two identical columns.

From Multiple of Column Added to Column of Determinant, performing this operation does not change the value of the determinant.

So a square matrix with a zero column has the same determinant as that with two identical columns.

$\blacksquare$