# Square Matrix with Duplicate Rows has Zero Determinant/Corollary

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

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

## Proof

If you add any row to a zero row, you get a square matrix with two identical rows.

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

So a square matrix with a zero row has the same determinant as that with two identical rows.

$\blacksquare$