If A= [ ll 0 & 1 1 & 0 ], then A^2= - Vidyadip

MCQ

If $A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$, then $A^2=$

A
$\left[\begin{array}{ll}1 & 1 \\ 0 & 0\end{array}\right]$
B
$\left[\begin{array}{ll}0 & 0 \\ 1 & 1\end{array}\right]$
C
$\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$
✓
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$

✓

Answer

Correct option: D.

$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$

Given
$
\begin{aligned}
& A=\left[\begin{array}{ll}
0 & 1 \\
1 & 0
\end{array}\right] \\
& A^2=A \times A=\left[\begin{array}{ll}
0 & 1 \\
1 & 0
\end{array}\right] \times\left[\begin{array}{ll}
0 & 1 \\
1 & 0
\end{array}\right] \\
& =\left[\begin{array}{ll}
0+1 & 0++0 \\
0+0 & 1+0
\end{array}\right] \\
& =\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right] .
\end{aligned}
$

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