Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2011 / Paper 1 / 13 / a / ii

Interchange the diagonal entries, negate the off-diagonal entries, and divide by the nonzero determinant. The matrix inverse isMultiplication by $A$ gives the identity matrix, since each diagonal product sum is $25-9=16$ and each off-diagonal product sum is zero.