If cosθ[(cosθ,sinθ),(-sinθ,cosθ)] + sinθ[(x,-cosθ),(cosθ,x)] = I2. Find x.

Question

If \(cos\theta\begin{bmatrix} cos\theta&sin\theta\\-sin\theta&cos\theta \end{bmatrix}+sin\theta\begin{bmatrix} x&-cos\theta\\cos\theta&x \end{bmatrix}\) = I₂. Find x.

Answer 1

L.H.S. =   \(cos\theta\begin{bmatrix} cos\theta&sin\theta\\-sin\theta&cos\theta \end{bmatrix}+sin\theta\begin{bmatrix} x&-cos\theta\\cos\theta&x \end{bmatrix}\)