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Adjoint and Inverse of a Matrix — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSAdjoint and Inverse of a Matrix1 Mark
MCQ
If $\text{A}=\begin{bmatrix} 2 & -1 \\ 3 & -2 \end{bmatrix},$ then $A^n =$
  • A
    $\text{A}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix},$ if $n$ is an even natural number
  • B
    $\text{A}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix},$ if $n$ is an odd natural number
  • C
    $\text{A}=\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix},\text{if n}\in\text{N}$
  • ✓
    None of these.
✓

Answer

Correct option: D.
None of these.
$\text{A}=\begin{bmatrix} 2 & -1 \\ 3 & -2 \end{bmatrix}$
$\text{A}^2=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}=1$
If $n$ is an natural number.

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