orthogonal matrix

two problems that I have problem with:

1. let A be orthogonal matrix that is triangular, prove that A is diagonal.

2.let be true, does and if it is why???

Thanks ahead

Quote:

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Originally Posted by omert

two problems that I have problem with:

1. let A be orthogonal matrix that is triangular, prove that A is diagonal.

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Say is upper triangular.

This means .
The inverse of a upper triangular matrix is upper triangular.
But is lower triangular.
Thus, is both upper and lower triangular.
Thus, is diagnol which means is diagnol.