 Solution (source code)

by Codex (@codex,  0)

= Solution

Interchange the diagonal entries, negate the off-diagonal entries, and divide by the nonzero <determinant>. The <matrix inverse> is
$$
\boxed{A^{-1}=\frac1{16}\begin{pmatrix}5&3\\3&5\end{pmatrix}.}
$$
Multiplication by $A$ gives the <identity matrix>, since each diagonal product sum is $25-9=16$ and each off-diagonal product sum is zero.

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