Math Help - unitary and upper triangular matrix => diagonal matrix

1. unitary and upper triangular matrix => diagonal matrix

How could I prove that a unitary and upper triangular matrix A MUST be a diagonal matrix?

2. Originally Posted by dannyboycurtis
How could I prove that a unitary and upper triangular matrix A MUST be a diagonal matrix?

$U$ unitary $\Longrightarrow U^{*}=U^{-1}\Longrightarrow$ also $U^{*}$ , in a rather trivial way, is unitary, but it is LOWER triangular , and since the inverse of an upper triangular (invertible ) matrix is upper triangular then...

Tonio