A is some MxN matrix Why is A singular A is some MxN matrix

A is some MxN matrix.

Why is A singular?

A is some MxN matrix. A^3 = 0 A is some MxN matrix.

Solution

A singular matrix has a determinant of zero and therefore has no inverse. If you are trying to solve a system of linear equations, for example, and the matrix is non-singular, then the solution set is unique. If it is singular, then you may end up with an empty solution set, or else one in which the solutions are not linearly independent.