What is a singular matrix?

A singular matrix is a matrix which has no inverse because its determinant is zero. If you recall, the inverse of a matrix is

1/ ad-bc multiplied by:

[ d -b ]

[-c a ]

If ad-bc = 0, then the inverse matrix would not exist because 1/0 is undefined, and hence it would be a singular matrix.

E.g.

[ 1 3]

[ 2 6]

Is a singular matrix because 6x1-3x2 = 0.