triangular 3 x 3 matrix.

triangular 3 x 3 matrix.

consider the upper triangular 3 x 3 matrix.
A=a b c
0 d e
0 0 f

For which values of a, b, c, d, e, and f is A invertible?
When is an upper triangular matrix invertible?
If an upper triangular matrix is invertible, is its inverse an upper triangular matrix as well?
When is a lower triangular matrix invertible?

triangular 3 x 3 matrix.