Is product of transpose of orthogonal & diagonal & orthogonal matrix = a diagonal matrix?

Question

Been a while since my first degree, and I can't seem to solve this kiddy-level question. Please indulge me:

A an orthogonal matrix, D a diagonal matrix.

is it true that $A^TDA = D$ ?

(where $^T$ is the transpose operator) Thanks.

Answer 1

Not true, a simple example: $A=\left(\begin{matrix} 0& 1\\ 1&0 \end{matrix}\right)$, $D=\left(\begin{matrix} 1& 0\\ 0&2 \end{matrix}\right)$.