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.

From Square Matrix with Duplicate Rows has Zero Determinant, that is zero.

Also see

 * Square Matrix with Duplicate Columns has Zero Determinant/Corollary