Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

Let \(A(\theta)=\left[\begin{array}{ll}\cos \theta & \sin \theta\\ -\sin \theta & \cos \theta\end{array}\right]\). Then which of the following is true

Options:

\(A(\theta)^{-1}\) does not exist

\((A(\theta))^{2022}=A(2022\theta)\)

\(A(\theta)\) is a symmetric matrix

\(A(\theta)\) is a skew-symmetric matrix

Correct Answer:

\((A(\theta))^{2022}=A(2022\theta)\)

Explanation:

By induction, note that \(A\left(\theta\right)^{n}=A(n \theta)\)