A nonsingular matrix is a mathematical term used to describe a square matrix that has an inverse. It is a matrix whose determinant is non-zero, meaning it has a unique solution in solving linear equations. There are several synonyms that can be used interchangeably with "nonsingular matrix". One commonly used term is "invertible matrix", which refers to a matrix that has an inverse and can be easily inverted. Another synonym is "non-degenerate matrix", as it implies that the matrix has non-zero determinants and is not degenerate in any way. Furthermore, "non-singular square matrix" can also be used to describe a matrix that has a unique solution and is not singular.