A) 1
B) 2
C) 4
D) No such 'a' exists
Correct Answer: A
Solution :
[A]\[3\,\,\times \,\,3\] matrix is equivalent to \[{{I}_{3}}\] if it is non-singular. |
Hence \[\left| \begin{matrix} 1 & 2a & 2 \\ 0 & -\,1 & 1 \\ a & 1 & 3 \\ \end{matrix} \right|=0\] |
\[\Rightarrow -\,4+a\,(2a+2)=0\] |
\[\Rightarrow 2{{a}^{2}}+2a-4=0\] |
\[\Rightarrow (a+2)\,\,(a-1)=0\to a=-\,2,\] 1 |
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