A) \[(-2,\,-2)\]
B) \[(2,\,-2)\]
C) \[(-2,\,2)\]
D) \[(2,\,2)\]
Correct Answer: A
Solution :
\[{{A}^{2}}=\left[ \begin{matrix} 2 & 2 \\ a & b \\ \end{matrix} \right]\,\left[ \begin{matrix} 2 & 2 \\ a & b \\ \end{matrix} \right]=\left[ \begin{matrix} 4+2a & 4+2b \\ 2a+ab & 2a+{{b}^{2}} \\ \end{matrix} \right]=0=\left[ \begin{matrix} 0 & 0 \\ 0 & 0 \\ \end{matrix} \right]\] \[\Rightarrow \,\,4+2a=0,4+2b=0,\]\[2a+ab=0,\] \[2a+{{b}^{2}}=0\]must be consistent. \[\Rightarrow \] \[a=-2\], \[b=-2\].
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