Question

For a given matrix A = $\begin{bmatrix} \cos\theta & - \sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$

which of the following statement holds good:

• A. A = A^–1" q Ī R
• B. A is symmetric, for q = (2n +1)$\frac{\pi}{2}$, n Ī I
• C. A is orthogonal matrix for q Ī R
• D. A is skew symmetric, for q = np, n Ī I

Answer 1

Answer: (C)

A is orthogonal matrix for q Ī R

Answer 2

For q = (2n +1)$\frac{\pi}{2}$

A=$\begin{bmatrix} 0 & \mp 1 \\ \pm 1 & 0 \end{bmatrix}$which is not symmetric for q = np

A = $\begin{bmatrix} \pm 1 & 0 \\ 0 & \pm 1 \end{bmatrix}$which is not skew symmetric

A² = $\begin{bmatrix} \cos 2\theta & - \sin 2\theta \\ \sin 2\theta & \cos 2\theta \end{bmatrix}$¹ I so A ¹ A^–1