Inverse of a Matrix and Its Applications — Formula Sheet

|A| = 0

|A| ≠ 0

M_ij = determinant of submatrix after removing row i and column j

C_ij = (-1)^(i+j) × M_ij

Adj A = (C_ij)^T

A⁻¹ = (1/|A|) × Adj A

AA⁻¹ = A⁻¹A = I

The inverse of a matrix A is a matrix A⁻¹ such that A × A⁻¹ = A⁻¹ × A = I (identity matrix).

If A is non-singular, the solution is X = A⁻¹B.