How to prove inverse of Matrix If you have an invertible upper triangular matrix $M$, how can you prove that $M^{-1}$ is also an upper triangular matrix? I already tried many things but don't know how to prove this. Please help!

The co-factor of any element above the diagonal is zero.Resaon :The matrix whose determinant is the co-factor will always be an upper triangular matrix with the determinant zero because either its last row is zero or its first column is zero or one of its diagonal element is zero.This can easily be verified. This will imply that the entries below the diagonal of the inverse of this matrix will all be zero.
