Question

If A = [a_ij] is a square matrix of order 2 such that a_ij = ${\displaystyle \{\begin{array}{l}1\text{,} \text{when i}\ne \text{j}\\ 0\text{,} \text{when} \text{i}=\text{j}\end{array},}$ then A² is ______.

पर्याय

• ${\displaystyle \left[\begin{array}{cc}1& 0\\ 1& 0\end{array}\right]}$

• ${\displaystyle \left|\begin{array}{cc}1& 1\\ 0& 0\end{array}\right|}$

• ${\displaystyle \left|\begin{array}{cc}1& 1\\ 1& 0\end{array}\right|}$

• ${\displaystyle \left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]}$

Answer 1

If A = [a_ij] is a square matrix of order 2 such that a_ij = ${\displaystyle \{\begin{array}{l}1\text{,} \text{when i}\ne \text{j}\\ 0\text{,} \text{when} \text{i}=\text{j}\end{array},}$ then A² is ${\displaystyle \underline{\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]}}$.

Explanation:

a_ij = ${\displaystyle \{\begin{array}{ll}1\text{,}& i\ne j\\ 0\text{,}& i=j\end{array},}$

then A = ${\displaystyle \left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]}$

and A² = ${\displaystyle \left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]}$