| Statement-1: lf \[A=\left[ \begin{matrix} a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c \\ \end{matrix} \right]\] then \[{{A}^{-1}}=\left[ \begin{matrix} \frac{1}{a} & 0 & 0 \\ 0 & \frac{1}{b} & 0 \\ 0 & 0 & \frac{1}{c} \\ \end{matrix} \right]\] |
| Statement-2: The inverse of a diagonal matrix is a diagonal matrix. |
A) Statement-1 and 2 are true and Statement-2 is correct explanation of Statement-1.
B) Statement-1 and 2 are true and Statement-2 is no correct explanation of Statement-1.
C) Statement-1 is true, statement-2 is false
D) Statement-1 is false, Statement-2 is true.
Correct Answer: B
Solution :
\[{{A}^{-1}}=\frac{1}{\det A}adjA\] \[=\frac{1}{abc}\left| \begin{matrix} bc & 0 & 0 \\ 0 & ca & 0 \\ 0 & 0 & ab \\ \end{matrix} \right|=\left| \begin{matrix} \frac{1}{a} & 0 & 0 \\ 0 & \frac{a}{b} & 0 \\ 0 & 0 & \frac{1}{c} \\ \end{matrix} \right|\] The inverse of a diagonal matrix is a diagonal matrix. Both true but statement-2 is not correct explanation of statement-1.
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