Ensure the matrix is square
Check that the determinant is nonzero
Use the formula for a 2×2 matrix: if (A=begin{pmatrix}a&b\c&dend{pmatrix}), then (A^{-1}=frac{1}{ad-bc}begin{pmatrix}d&-b\-c&aend{pmatrix})
For larger matrices, form the augmented matrix ([A mid I])
Apply row operations to transform (A) into the identity matrix
The matrix on the right becomes (A^{-1})
Alternatively, compute the adjugate matrix and divide by the determinant
Verify the result by multiplying (A cdot A^{-1} = I)