Class 12 Maths · Matrices · Assertion Reason #29

Assertion: If A=\(\begin{bmatrix}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{bmatrix}\), then A²=\(\begin{bmatrix}\cos2\theta & \sin2\theta\\-\sin2\theta & \cos2\theta\end{bmatrix}\). Reason: For this rotation matrix and every positive integer n, Aⁿ=\(\begin{bmatrix}\cos n\theta & \sin n\theta\\-\sin n\theta & \cos n\theta\end{bmatrix}\).