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.