Solution
= Solution
The <determinant> is an <alternating multilinear map> of its rows, so exchanging two rows gives \b[the negative of the original determinant]: $\det A\mapsto-\det A$. This also holds when the <determinant> is zero.
= Solution
The <determinant> is an <alternating multilinear map> of its rows, so exchanging two rows gives \b[the negative of the original determinant]: $\det A\mapsto-\det A$. This also holds when the <determinant> is zero.