A) \[\left[ \begin{matrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} {{a}^{2}} & 0 & 0 \\ 0 & ab & 0 \\ 0 & 0 & ac \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 1/a & 0 & 0 \\ 0 & 1/b & 0 \\ 0 & 0 & 1/c \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} -a & 0 & 0 \\ 0 & -b & 0 \\ 0 & 0 & -c \\ \end{matrix} \right]\]
Correct Answer: C
Solution :
\[A=\left[ \begin{matrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \\ \end{matrix} \right]\] \[\therefore \] \[adj\,(A)=\,\left[ \begin{matrix} bc & 0 & 0 \\ 0 & ca & 0 \\ 0 & 0 & ab \\ \end{matrix} \right]\] and \[|A|\,=abc\] \[\therefore \] \[{{A}^{-1}}=\frac{adj\,(A)}{|A|}=\left[ \begin{matrix} 1/a & 0 & 0 \\ 0 & 1/b & 0 \\ 0 & 0 & 1/c \\ \end{matrix} \right]\]
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