# Math Help - I have to show this proof for the matrix inverse theorem

1. ## I have to show this proof for the matrix inverse theorem

I cannot use the matrix inverse theorem, yet I have to show this, thanks in advance.

If the equation Ax = b has at least one solution for each b in Rn, then the equation Ax = 0 has only the trivial solution.

thanks in advance

2. ## Re: I have to show this proof for the matrix inverse theorem

Isn't it because the only matrix you could multiply x by to get the a zero vector is the zero matrix, and that the determinant of the zero matrix is 0?