## Differential Equations and Linear Algebra (4th Edition)

We know that the determinant of a matrix $\left[\begin{array}{rr} a & b \\ c &d \\ \end{array} \right]$ is $D=ad-bc$. Also, a matrix is non-invertible if $D=0$. here $D=x^2y-xy^2=xy(y-x)$. Thus if it is non-invertible then $x=0$, $y=0$ or $x=y$, thus the statement is false.