College Algebra (6th Edition)

The 2x2 matrix $A$ is invertible if and only if $ad-bc\neq 0$. If $ad-bc=0$, then $A$ does not have a multiplicative inverse. If $A=\left[\begin{array}{ll} a & b\\ c & d \end{array}\right]$, then $A^{-1}=\displaystyle \frac{1}{ad-bc}\left[\begin{array}{ll} d & -b\\ -c & a \end{array}\right]$. -------- So, for example, $\left[\begin{array}{ll} 1 & 0\\ 0 & 1 \end{array}\right]$ and $\left[\begin{array}{ll} -1 & 0\\ 0 & -1 \end{array}\right]$ both have inverses, but their sum, $\left[\begin{array}{ll} 0 & 0\\ 0 & 0 \end{array}\right]$ does not. True.