Find the inverse of the matrix if it exists. $$\left[ \begin{array} { l l l }
2 & 0 & 0 \
0 & 9 & 0 \
0 & 0 & 8
\end{array} \right]$$
A) $$\left[ \begin{array} { c c c }
1 & \frac { 1 } { 9 } & 1 \
\frac { 1 } { 8 } & 0 & - 2 \
0 & 1 & \frac { 1 } { 2 }
\end{array} \right]$$
B) $$\left[ \begin{array} { c c c }
\frac { 1 } { 2 } & 0 & 0 \
0 & \frac { 1 } { 9 } & 0 \
0 & 0 & \frac { 1 } { 9 }
\end{array} \right]$$
C) $$\left[ \begin{array} { c c c }
0 & 0 & \frac { 1 } { 2 } \
0 & \frac { 1 } { 8 } & 0 \
\frac { 1 } { 9 } & 0 & 0
\end{array} \right]$$
D) $$\left[ \begin{array} { c c c }
\frac { 1 } { 2 } & 0 & 0 \
0 & \frac { 1 } { 9 } & 0 \
0 & 0 & \frac { 1 } { 8 }
\end{array} \right]$$
E) Does not exist

Question

Find the inverse of the matrix if it exists. $$\left[ \begin{array} { l l l } 
2 & 0 & 0 \
0 & 9 & 0 \
0 & 0 & 8
\end{array} \right]$$
A) $$\left[ \begin{array} { c c c } 
1 & \frac { 1 } { 9 } & 1 \
\frac { 1 } { 8 } & 0 & - 2 \
0 & 1 & \frac { 1 } { 2 }
\end{array} \right]$$
B) $$\left[ \begin{array} { c c c } 
\frac { 1 } { 2 } & 0 & 0 \
0 & \frac { 1 } { 9 } & 0 \
0 & 0 & \frac { 1 } { 9 }
\end{array} \right]$$
C) $$\left[ \begin{array} { c c c } 
0 & 0 & \frac { 1 } { 2 } \
0 & \frac { 1 } { 8 } & 0 \
\frac { 1 } { 9 } & 0 & 0
\end{array} \right]$$
D) $$\left[ \begin{array} { c c c } 
\frac { 1 } { 2 } & 0 & 0 \
0 & \frac { 1 } { 9 } & 0 \
0 & 0 & \frac { 1 } { 8 }
\end{array} \right]$$
E) Does not exist

Quizplus · Accepted Answer

The inverse of a diagonal matrix is another diagonal matrix with the reciprocals of the original diagonal elements.

Find the Inverse of the Matrix If It Exists [200090008]\left[ \begin{array} { l l l } 2 & 0 & 0 \\0 & 9 & 0 \\0 & 0 & 8\end{array} \right]​200​090​008​​

Find the Inverse of the Matrix If It Exists $\left[ \begin{array} { l l l } 2 & 0 & 0 \\0 & 9 & 0 \\0 & 0 & 8\end{array} \right]$