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MCQMediumJEE Main 2024 · 27 January, Shift 1Algebra of Matrices

Mathematics Question from JEE Main 2024 · 27 January, Shift 1

Given f(x)=[cos⁡x−sin⁡x0sin⁡xcos⁡x0001]f(x)=\begin{bmatrix}\cos x & -\sin x & 0\\ \sin x & \cos x & 0\\ 0 & 0 & 1\end{bmatrix} Evaluate: Statement I: f(−x)f(-x) is the inverse of f(x)f(x). Statement II: f(x)⋅f(y)=f(x+y)f(x)\cdot f(y)=f(x+y).

  • A

    I is false, II is true

  • B

    Both I and II are false

  • C

    I is true, II is false

  • D

    Both I and II are true

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