If A = , then A 2 is equal to

Matrices — Class 12 Maths Solution

exemplar objective MCQ NCERT,Exemp,Q.no.58,Page 60

Question

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

(a) $\left[ {\begin{array}{llllllllllllllllllll}0&1\\1&0\end{array}} \right]$
(b) $\left[ {\begin{array}{llllllllllllllllllll}1&0\\1&0\end{array}} \right]$
(c) $\left[ {\begin{array}{llllllllllllllllllll}0&1\\0&1\end{array}} \right]$
(d) $\left[ {\begin{array}{llllllllllllllllllll}1&0\\0&1\end{array}} \right]$ ✓ Correct

Step-by-step Solution

${A^2} = A \cdot A = \left[ {\begin{array}{llllllllllllllllllll}0&1\\1&0\end{array}} \right] \cdot \left[ {\begin{array}{llllllllllllllllllll}0&1\\1&0\end{array}} \right]$

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

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