If I = [(1,0)(0,1)], J =[(0,1)(-1,0)] and B = [(cos θ, sin θ)(-sin θ,cos θ)] then B equals : ​

Question

If I = \(\begin{bmatrix} 1 & 0 \\[0.3em] 0 & 1 \end{bmatrix}\), J = \(\begin{bmatrix} 0 & 1 \\[0.3em] -1 & 0 \end{bmatrix}\) and B =\(\begin{bmatrix} cos\,\theta & sin\,\theta \\[0.3em] -sin\,\theta & cos\,\theta \end{bmatrix}\), then B equals :

A. I cos θ + J sin θ 

B. I sin θ + J cos θ 

C. I cos θ – J sin θ 

D. – I cos θ + J sin θ

Answer 1

(A). I cos θ + J sin θ

I = \(\begin{bmatrix} 1 & 0 \\[0.3em] 0 & 1 \end{bmatrix}\)

Option (A) is the answer.