If A= [a_ i j ] is a square matrix of order 2 such that a_ i j = … - Vidyadip

MCQ

If $A=\left[a_{i j}\right]$ is a square matrix of order $2$ such that $a_{i j}=\left\{\begin{array}{l}1, \text { when } i \neq j \\ 0, \text { when } i=j\end{array}\right.$, then $A^2$ is

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

✓

Answer

Correct option: D.

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

We have, $ A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$
$\therefore A^2=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$
$=\left[\begin{array}{ll}0+1 & 0+0 \\ 0+0 & 1+0\end{array}\right]$
$=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$

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