Write the inverse of the matrix [(cosθ ,sinθ)(-sinθ,cosθ)].

Question

Write the inverse of the matrix \(\begin{bmatrix} cos\,\theta & sin\,\theta \\[0.3em] -sin\,\theta & cos\,\theta \\[0.3em] \end{bmatrix}.\)

Answer 1

Let A = \(\begin{bmatrix} cos\,\theta & sin\,\theta \\[0.3em] -sin\,\theta & cos\,\theta \\[0.3em] \end{bmatrix}\)

|A| = cos²θ + sin²θ = 1 ≠ 0

Since, |A| ≠ 0

Now,

A^-1 = \(\frac{Adj\,A}{|A|}\)