If matrix A = [ a i j ] 2 × 2 , where a i j = { 1 if i j 0 if i = j then A 2 is equal to:

Question

If matrix $A = {[a_{i j}]}_{2 \times 2},$ where $a_{i j} =$ ${\begin{matrix} 1 & if i \neq j \\ 0 & if i = j \end{matrix}$ then $A^{2}$ is equal to:

Smart Achievers · Accepted Answer

(1)

Ans. $I$

Explanation:

We have, $A = {[a_{i j}]}_{2 \times 2}$

where $a_{i j} =$ ${\begin{matrix} 1, & i \neq j \\ 0, & i = j \end{matrix}$

$∴$ $A = [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}]$

and $A^{2} = [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}] [\begin{matrix} 0 & 1 \\ 1 & 0 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = I$

Solution

Q.
If matrix $A = {[a_{i j}]}_{2 \times 2},$ where $a_{i j} =$ ${\begin{matrix} 1 & if i \neq j \\ 0 & if i = j \end{matrix}$ then $A^{2}$ is equal to:

1 $I$

2 $A$

3 $0$

4 none of these

Want Us to Email you About Special Offers & Updates?