Question

Ortogonal matrix.

Answer 1

I have to show that \[\left[\begin{matrix}0 &1&-1\\ 1 & -1&0 \\0&0&1\end{matrix}\right]\]
not are orthogonal.
Is it enough to show that \[A^{-1}\neq A^T\]

Answer 2

A matrix A is orthogonal if AA(t)=I and A(t)A=I
A(t) -> transpose of A
I -> unit matrix. Show that either of those conditions is not true.

Answer 3

Thank you. And when the matrix is not orthogonal it is not length preserving. Agree?

Answer 4

That I'm not sure about, it's been a while since i did linear algebra :/