In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that:
AB = BA = I (where I is the Identity Matrix).
Otherwise, in life, it refers to the case where something can be transformed into something else and transformed back.
Sandy: I know, nonsingularly so. Put a few drinks in her and you can get her on her back and yet in the morning she still gets up and cooks you breakfast.