Inverse of 2x2 Matrix

Theorem

Let $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$

Then

• $A$ is invertible if and only if $ad-bc\ne 0$

$$A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$$