Question

If $A = \begin{bmatrix} \cos\theta & - \sin\theta \\ \sin\theta & \cos\theta \end{bmatrix},$ then which of the following statement is not correct

• A. A is orthogonal matrix
• B. $A^{T}$ is orthogonal matrix
• C. Determinant $A = 1$
• D. A is not invertible

Answer 1

Answer: (B)

$A^{T}$ is orthogonal matrix

Answer 2

$|A| = 1 \neq 0,$ therefore A is invertible. Thus (4) is not correct