The inverse of the matrix $ A=\left[\begin{array}{lll}2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4\end{array}\right] $ is

Question

The inverse of the matrix $ A=\left[\begin{array}{lll}2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4\end{array}\right] $ is, $ \left[\begin{array}{lll}2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4\end{array}\right] $, $ \frac{1}{24}\left[\begin{array}{lll}1 / a & 0 & 0 \ 0 & 1 / b & 0 \ 0 & 0 & 1 / c\end{array}\right] $, $ \frac{1}{24}\left[\begin{array}{lll}2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4\end{array}\right] $, $ \frac{1}{24}\left[\begin{array}{llll}1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1\end{array}\right] $

MARKS App · Accepted Answer

Given that $ A=\left[\begin{array}{lll}2 & 0 & 0 \ 0 & 3 & 0 \ 0 & 0 & 4\end{array}\right] $ Now $ A^{-1}=\left[\begin{array}{ccc}1 / 2 & 0 & 0 \ 0 & 1 / 3 & 0 \ 0 & 0 & 1 / 4\end{array}\right] $ If $ A=\left[\begin{array}{ccc}a & 0 & 0 \ 0 & b & 0 \ 0 & 0 & c\end{array}\right] $, then $ A^{-1}=\left[\begin{array}{ccc}1 / a & 0 & 0 \ 0 & 1 / b & 0 \ 0 & 0 & 1 / c\end{array}\right] $ When $ a \neq 0, b \neq 0, c \neq 0 $

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