## Linear Algebra: A Modern Introduction

$a^2b+ab^2$
By using the cofactor expansion along the first row: $det\begin{vmatrix} a& b&0\\ 0&a &b\\ a&0 &b \end{vmatrix}$ $=a\times det\begin{vmatrix} a&b\\ 0 &b \end{vmatrix}-b\times det\begin{vmatrix} 0 &b\\ a&b \end{vmatrix}+0\times det\begin{vmatrix} 0&a\\ a&0 \end{vmatrix}$ $=a(ab-0)-b(0-ab)+0$ $=a^2b+ab^2$