If $A=\begin{bmatrix}a&b\\c&d\end{bmatrix}$ and $\Delta=ad-bc\ne0$, then $A^{-1}=\Delta^{-1}\begin{bmatrix}d&-b\\-c&a\end{bmatrix}$. Multiplying verifies both inverse identities. When $\Delta=0$, no inverse exists.
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