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  • If matrix A = [a_ij] , where aij = 1 if i ≠ j aij = 0 if i = j, then A2 is equal to A. I B. A C. 0 D. None of these

If matrix A=[a_{ij}]_{2\times 2}, where aij = 1 if i ≠ j, aij = 0 if i = j, then A^2 is equal to
A. I
B. A
C. 0
D. None of these

Answers (1)

Solution

We are given that,

a\textsubscript{11} = 0 , a\textsubscript{12} = 1 , a\textsubscript{21} = 1 and a\textsubscript{22} = 0

\begin{array}{l} \therefore 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] \end{array}

According to the rule of matrix multiplication:

\begin{array}{l} \therefore A^2=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right] \\ \end{array}  which matches with option (A)
Hence we can say that,

∴ Option (A) is the correct answer.

Posted by

infoexpert22

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