Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Matrices

Question:

If \(P\left(x\right)=\left[\begin{array}{ll}\cos x & \sin x\\ -\sin x& \cos x\end{array}\right]\) and \(n \in \mathbb{N}\) then which of the following holds

Options:

\(P\left(x\right)^{n}=P\left(x^{n}\right)\)

\(P\left(x^{n}\right)=P\left(nx\right)\)

\(P\left(x^{n}\right)=P\left(x^{n-1}\right)\)

\(P\left(x^{n}\right)=nP\left(x\right)\)

Correct Answer:

\(P\left(x^{n}\right)=P\left(nx\right)\)

Explanation:

Multiply \(P\left(x\right)\) with \(P\left(x\right)\) and try to see what are we getting