If A= [ cc 3 & 1 -1 & 2 ], then A^2= - Vidyadip

MCQ

If $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$, then $A^2=$

✓
$\left[\begin{array}{cc}8 & 5 \\ -5 & 3\end{array}\right]$
B
$\left[\begin{array}{cc}8 & -5 \\ 5 & 3\end{array}\right]$
C
$\left[\begin{array}{cc}8 & -5 \\ -5 & -3\end{array}\right]$
D
$\left[\begin{array}{cc}8 & -5 \\ -5 & 3\end{array}\right]$

✓

Answer

Correct option: A.

$\left[\begin{array}{cc}8 & 5 \\ -5 & 3\end{array}\right]$

$\begin{aligned} & A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right] \\ & A^2=A \times A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right] \\ & =\left[\begin{array}{cc}9+(-1) & 3+2 \\ -3-2 & -1+4\end{array}\right] \\ & =\left[\begin{array}{cc}8 & 5 \\ -5 & 3\end{array}\right] .\end{aligned}$

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