For a square m × m matrix A,v the inverse matrix Av⁻¹is also an m × m matrix such that Av⁻¹Av = Iv = AAv⁻¹, where Iv is the identity matrix. If a matrix has an inverse, then its inverse is unique and the matrix is said to be nonsingular. If an inverse does not exist, the matrix is said to be singular. A nonsingular matrix has a nonzero value for its determinant; a singular matrix has a determinant value equal to zero.  Matrices and matrix algebra.