Solve for p

The value (a^-1) is the inverse of a, and all non-zero real numbers have an inverse. It would be nice to have a similar idea for square matrices.

Say that

Ap = q

for column vectors p and q and n×n matrix A .

If all know are A and q, is it possible to figure out what p is? For example, say that you know that

1 2 0 1

p

=

5 2

Try to figure out p from the following. Keep changing the elements of p until the result is q.

A				p			=	q