Hi guys, can anyone help me with this question please. I have shown that P is an orthogonal matrix as P is invertible therefore it is orthogonal but im struggling with the rest of the question.

Let

P= cos θ -sinθ

sin θ cos θ

Show that P is an orthogonal matrix.

Let A =

d e

e f

Determine B= P(transposed)AP.

Show that the choice

θ= 1/2 tan-1 {2e/d-f}

will make B is a diagonal matrix.

How is the result modified for the case when d= f?

Thanks