A) \[{{a}^{2}}I+abA\]
B) \[{{a}^{2}}I+2abA\]
C) \[{{a}^{2}}I+{{b}^{2}}A\]
D) None of these
Correct Answer: B
Solution :
[b] \[{{(aI+bA)}^{2}}={{a}^{2}}{{I}^{2}}+{{b}^{2}}{{A}^{2}}+2ab\,AI\] \[={{a}^{2}}{{I}^{2}}+{{b}^{2}}{{A}^{2}}+2abA\] But \[{{A}^{2}}=\left[ \begin{matrix} 0 & 0 \\ 0 & 0 \\ \end{matrix} \right]\therefore \,{{(aI+bA)}^{2}}={{a}^{2}}I+2abA\].
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