\[\left|\mathbf{A}\right|=\det(\mathbf{A})=\left|\begin{matrix}a_{11}&a_{12}&%
\dots&a_{1n}\\
a_{21}&a_{22}&\dots&a_{2n}\\
\vdots&\vdots&\ddots&\vdots\\
a_{n1}&a_{n2}&\dots&a_{nn}\end{matrix}\right|,\]