Study guide and 3 practice problems on:

## Matrix inverses

The matrix $\bfB$ is the matrix inverse of $\bfA$ if $\bfA \bfB = \bfI$ and $\bfB \bfA = \bfI.$
The matrix inverse of $\bfA$ is denoted $\bfA^{-1}$.
The inverse of a $2\times2$ matrix is given by swapping the diagonal entries, negating the off-diagonal entries, and dividing by the determinant: $$\begin{pmatrix}a&b\\c&d\end{pmatrix}^{-1} = \frac{1}{ad-bc} \begin{pmatrix}d & -b \\ -c & a\end{pmatrix}$$
To find the inverse of a $3 \times 3$ matrix,
1. Compute the minors of each element
2. Negate every other element, according to a checkerboard pattern
3. Take the transpose
4. Divide by the determinant of the original matrix