If $a, b, c$ are non-zero real numbers, then the inverse of the $\operatorname{matrix} A=\left[\begin{array}{lll}\mathrm{a} & 0 & 0 \\ 0 & \mathrm{~b} & 0 \\ 0 & 0 & \mathrm{c}\end{array}\right]$ is equal to

• Correct answer
  A

  $\left[\begin{array}{lll}\mathrm{a}^{-1} & 0 & 0 \\ 0 & \mathrm{~b}^{-1} & 0 \\ 0 & 0 & \mathrm{c}^{-1}\end{array}\right]$
• B

  $\frac{1}{\mathrm{abc}}\left[\begin{array}{lll}\mathrm{a}^{-1} & 0 & 0 \\ 0 & \mathrm{~b}^{-1} & 0 \\ 0 & 0 & \mathrm{c}^{-1}\end{array}\right]$
• C

  $\frac{1}{\mathrm{abc}}\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$
• D

  $\frac{1}{\mathrm{abc}}\left[\begin{array}{lll}\mathrm{a} & 0 & 0 \\ 0 & \mathrm{~b} & 0 \\ 0 & 0 & \mathrm{c}\end{array}\right]$

Hence, the correct answer is option: 'A'.