defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Matrices Operations on Matrices
If \(A=\left(\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right)\) and \(\theta=\frac{2 \pi}{7}\), then A100 = A × A × ..... (100 times) is equal to
1
\(\left(\begin{array}{cc} \cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta \end{array}\right)\)
2
\(\left(\begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right)\)
3
\(\left(\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right)\)
4
\(\left(\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right)\)