Question

Let $n$ be a positive integer then if $A=\left[\begin{array}{cc}cos\theta & sin\theta \\ sin\theta & cos\theta \end{array}\right]$, find the value of $A^n=$

• A. $\left[\begin{array}{cc}cos\theta & -sin\theta \\ sin\theta & cos\theta \end{array}\right]$
• B. $\left[\begin{array}{cc}cos\theta & -sin\theta \\ -sin\theta & cos\theta \end{array}\right]$
• C. $\left[\begin{array}{cc}cos\theta & sinn\theta \\ sinn\theta & cosn\theta \end{array}\right]$
• D. $\left[\begin{array}{cc}cosn\theta & cosn\theta \\ sinn\theta & sinn\theta \end{array}\right]$

Answer 1

The correct option is C $\left[\begin{array}{cc}cos\theta & sinn\theta \\ sinn\theta & cosn\theta \end{array}\right]$