Provide an appropriate response.
-Let $\mathrm { A } = \left[ \begin{array} { l l } \mathrm { c } & 0 \ 0 & \mathrm {~b} \end{array} \right]$, where $\mathrm { c }$ and $\mathrm { b }$ are nonzero constants. Find $\mathrm { A } ^ { - 1 }$.
A)
$$\left[ \begin{array} { l l }
\frac { 1 } { c } & 0 \
0 & \frac { 1 } { b }
\end{array} \right]$$

B)
$\left[\begin{array}{ll}
0 & \mathrm{c} \
\mathrm{b} & 0
\end{array}\right]$

C)
$\left[\begin{array}{l}
\frac{1}{c} 1 \
1 \frac{1}{b}
\end{array}\right]$

D)

$\left[\begin{array}{ll}
\mathrm{c} & 0 \
0 & \mathrm{~b}
\end{array}\right]$

Question

Provide an appropriate response.
-Let $\mathrm { A } = \left[ \begin{array} { l l } \mathrm { c } & 0 \ 0 & \mathrm {~b} \end{array} \right]$, where $\mathrm { c }$ and $\mathrm { b }$ are nonzero constants. Find $\mathrm { A } ^ { - 1 }$.
A)
$$\left[ \begin{array} { l l } 
\frac { 1 } { c } & 0 \
0 & \frac { 1 } { b }
\end{array} \right]$$

B)
$\left[\begin{array}{ll}
0 & \mathrm{c} \
\mathrm{b} & 0
\end{array}\right]$

C)
$\left[\begin{array}{l}
\frac{1}{c} 1 \
1 \frac{1}{b}
\end{array}\right]$

D)

$\left[\begin{array}{ll}
\mathrm{c} & 0 \
0 & \mathrm{~b}
\end{array}\right]$

Quizplus · Accepted Answer

The inverse of a diagonal matrix $\left[ \begin{array} { l l } c & 0 \ 0 & b \end{array} \right]$ is obtained by taking the reciprocal of each nonzero diagonal element, resulting in $\left[ \begin{array} { l l } \frac { 1 } { c } & 0 \ 0 & \frac { 1 } { b } \end{array} \right]$.

Provide an Appropriate Response A=[c00 b]\mathrm { A } = \left[ \begin{array} { l l } \mathrm { c } & 0 \\ 0 & \mathrm {~b} \end{array} \right]A=[c0​0 b​]

Provide an Appropriate Response $\mathrm { A } = \left[ \begin{array} { l l } \mathrm { c } & 0 \\ 0 & \mathrm {~b} \end{array} \right]$