If A= 2 & -1 3 & -2 , then A^n= - Vidyadip

MCQ

If $\text{A}=\begin{bmatrix} 2 & -1 \\ 3 & -2 \end{bmatrix},$ then $A^n=$

✓
$\text{A}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix},$ 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
$\text{A}=\begin{bmatrix} -1 & 0 \\ 0 & 1 \end{bmatrix},$ if $n\in\text{N}$
D
None of these.

✓

Answer

Correct option: A.

$\text{A}=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix},$ if $n$ is an even natural number

$\text{A}=\begin{bmatrix} 2 & -1 \\ 3 & -2 \end{bmatrix}$
$\text{A}^2=\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}=1$
If $n$ is an natural number.

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