A singular matrix, also called degenerate matrix, is a square matrix whose determinant is zero and that doesn't have a matrix inverse. It's rare to come across a singular matrix because a square matrix selected from a continuous uniform distribution on its entries will almost never be singular.
The opposite of a singular matrix is a non-singular matrix or non-degenerate matrix, which is also a square matrix but whose determinant is not equal to zero. Matrix inversion is the process of calculating the matrix Y that satisfies the prior equation for a given invertible matrix X. A matrix is invertible if it has an inverse, is non-singular or is non-degenerate.