If $F(\alpha ) = \begin{bmatrix} \cos \alpha & - \sin \alpha & 0 \\ \sin \alpha & \cos \alpha & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and $G(\beta ) = \begin{bmatrix} \cos \beta & 0 & \sin \beta \\ 0 & 1 & 0 \\ - \sin \beta & 0 & \cos \beta \end{bmatrix}$,then $[F(\alpha ) G(\beta )]^{-1} = $

  • A
    $F(\alpha ) - G(\beta )$
  • B
    $- F(\alpha ) - G(\beta )$
  • C
    $[F(\alpha )]^{-1} [G(\beta )]^{-1}$
  • D
    $[G(\beta )]^{-1} [F(\alpha )]^{-1}$

Explore More

Similar Questions

If $A$ is a matrix of order $2$ and $I$ is the identity matrix of order $2$ such that $A^2 - 4A + 3I = 0$,then $(A + 3I)^{-1} =$

Let $P = \begin{bmatrix} 3 & -1 & -2 \\ 2 & 0 & \alpha \\ 3 & -5 & 0 \end{bmatrix}$ where $\alpha \in R$. Suppose $Q = [q_{ij}]$ is a matrix satisfying $PQ = kI_3$ for some non-zero $k \in R$. If $q_{23} = -\frac{k}{8}$ and $|Q| = \frac{k^2}{2}$,then $\alpha^2 + k^2$ is equal to?

If $A = \begin{bmatrix} 2 & 3 \\ 1 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 0 \\ 3 & 1 \end{bmatrix}$,then $B^{-1} A^{-1} = $

Find the inverse of the matrix,if it exists: $\left[\begin{array}{cc}3 & -1 \\ -4 & 2\end{array}\right]$

If $A = \begin{bmatrix} 1 & -1 & 1 \\ 0 & 2 & -3 \\ 2 & 1 & 0 \end{bmatrix}$,$B = \text{adj}(A)$,and $C = 5A$,then find the value of $\frac{|\text{adj}(B)|}{|C|}$.

Difficult
View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo