A) \[{{a}^{27}}\]
B) \[{{a}^{9}}\]
C) \[{{a}^{6}}\]
D) \[{{a}^{2}}\]
Correct Answer: C
Solution :
[c] \[Cofactor\,\,matrix=\left[ \begin{matrix} {{a}^{2}} & 0 & 0 \\ 0 & {{a}^{2}} & 0 \\ 0 & 0 & {{a}^{2}} \\ \end{matrix} \right]\] \[\therefore \] adj A = (cofactor matrix)\[=\left[ \begin{matrix} {{a}^{2}} & 0 & 0 \\ 0 & {{a}^{2}} & 0 \\ 0 & 0 & {{a}^{2}} \\ \end{matrix} \right]\] \[\therefore \left| adj\,\,A \right|=\left[ \begin{matrix} {{a}^{2}} & 0 & 0 \\ 0 & {{a}^{2}} & 0 \\ 0 & 0 & {{a}^{2}} \\ \end{matrix} \right]={{a}^{6}}\]
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