Question

Prove that \(\begin{bmatrix}cos^2\alpha&cos\alpha sin\alpha\\[0.3em]cos\alpha sin\alpha&sin^2\alpha\end{bmatrix}\)\(\begin{bmatrix}cos^2\beta&cos\beta sin\beta\\[0.3em]cos\beta sin\beta& sin^2\beta\end{bmatrix}\)  = 0 when α - β = (2m - 1)π/2, m ∈  N

Answer 1

LHS = \(\begin{bmatrix}cos^2\alpha&cos\alpha sin\alpha\\[0.3em]cos\alpha sin\alpha&sin^2\alpha\end{bmatrix}\)\(\begin{bmatrix}cos^2\beta&cos\beta sin\beta\\[0.3em]cos\beta sin\beta& sin^2\beta\end{bmatrix}\)