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If $a, b, c$ are non-zero real numbers, then the inverse of the
matrix $\mathrm{A}=\left[\begin{array}{lll}\mathrm{a} & 0 & 0 \\ 0 & \mathrm{~b} & 0 \\ 0 & 0 & \mathrm{c}\end{array}\right]$ is equal to
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matrix $\mathrm{A}=\left[\begin{array}{lll}\mathrm{a} & 0 & 0 \\ 0 & \mathrm{~b} & 0 \\ 0 & 0 & \mathrm{c}\end{array}\right]$ is equal to
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Verified Answer
The correct answer is:
$\left[\begin{array}{lll}a^{-1} & 0 & 0 \\ 0 & b^{-1} & 0 \\ 0 & 0 & c^{-1}\end{array}\right]$
$\mathrm{A}=\left[\begin{array}{lll}\mathrm{a} & 0 & 0 \\ 0 & \mathrm{~b} & 0 \\ 0 & 0 & \mathrm{c}\end{array}\right]$
$\mathrm{A}^{-1}=\left[\begin{array}{ccc}\frac{1}{\mathrm{a}} & 0 & 0 \\ 0 & \frac{1}{\mathrm{~b}} & 0 \\ 0 & 0 & \frac{1}{\mathrm{c}}\end{array}\right]=\left[\begin{array}{ccc}\mathrm{a}^{-1} & 0 & 0 \\ 0 & \mathrm{~b}^{-1} & 0 \\ 0 & 0 & \mathrm{c}^{-1}\end{array}\right]$
$\mathrm{A}^{-1}=\left[\begin{array}{ccc}\frac{1}{\mathrm{a}} & 0 & 0 \\ 0 & \frac{1}{\mathrm{~b}} & 0 \\ 0 & 0 & \frac{1}{\mathrm{c}}\end{array}\right]=\left[\begin{array}{ccc}\mathrm{a}^{-1} & 0 & 0 \\ 0 & \mathrm{~b}^{-1} & 0 \\ 0 & 0 & \mathrm{c}^{-1}\end{array}\right]$
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