Q40 / 60 · IAT (IISER) 2022 · Mathematics
Let $A$ be the matrix
$\left[\begin{array}{ccc}<br/>\cos \theta & 0 & -\sin \theta \\<br/>1 & 1 & 1 \\<br/>\sin \theta & 0 & \cos \theta<br/>\end{array}\right]$
For any natural number $k$, the determinant of $A^k$ is
$\left[\begin{array}{ccc}<br/>\cos \theta & 0 & -\sin \theta \\<br/>1 & 1 & 1 \\<br/>\sin \theta & 0 & \cos \theta<br/>\end{array}\right]$
For any natural number $k$, the determinant of $A^k$ is
- A$(-1)^k$
- Correct answerB$1$
- C$0$
- D$-1$
Hence, the correct answer is option: 'B'.