Find the inverse of the matrix (if it exists). $$\left[ \begin{array} { l l }
3 & 0 \
0 & 4
\end{array} \right]$$
A) $$\left[ \begin{array} { l l }
\frac { 1 } { 4 } & 0 \
0 & \frac { 1 } { 4 }
\end{array} \right]$$
B) $$\left[ \begin{array} { l l }
\frac { 1 } { 4 } & 0 \
0 & 0
\end{array} \right]$$
C) $$\left[ \begin{array} { c c }
0 & \frac { 1 } { 4 } \
\frac { 1 } { 4 } & 0
\end{array} \right]$$
D) $$\left[ \begin{array} { l l }
\frac { 1 } { 4 } & 0 \
0 & \frac { 1 } { 3 }
\end{array} \right]$$
E) $$\left[ \begin{array} { l l }
\frac { 1 } { 3 } & 0 \
0 & \frac { 1 } { 4 }
\end{array} \right]$$

Question

Find the inverse of the matrix (if it exists).​ $$\left[ \begin{array} { l l } 
3 & 0 \
0 & 4
\end{array} \right]$$ ​
A)​ $$\left[ \begin{array} { l l } 
\frac { 1 } { 4 } & 0 \
0 & \frac { 1 } { 4 }
\end{array} \right]$$
B)​ $$\left[ \begin{array} { l l } 
\frac { 1 } { 4 } & 0 \
0 & 0
\end{array} \right]$$
C)​ $$\left[ \begin{array} { c c } 
0 & \frac { 1 } { 4 } \
\frac { 1 } { 4 } & 0
\end{array} \right]$$
D)​ $$\left[ \begin{array} { l l } 
\frac { 1 } { 4 } & 0 \
0 & \frac { 1 } { 3 }
\end{array} \right]$$
E)​ $$\left[ \begin{array} { l l } 
\frac { 1 } { 3 } & 0 \
0 & \frac { 1 } { 4 }
\end{array} \right]$$

Quizplus · Accepted Answer

The inverse of a diagonal matrix is simply the diagonal matrix with each diagonal element replaced by its reciprocal. Thus, the inverse of $\left[ \begin{array} { l l } 3 & 0 \ 0 & 4 \end{array} \right]$ is $\left[ \begin{array} { l l } \frac { 1 } { 3 } & 0 \ 0 & \frac { 1 } { 4 } \end{array} \right]$.

Find the Inverse of the Matrix (If It Exists) [3004]\left[ \begin{array} { l l } 3 & 0 \\0 & 4\end{array} \right][30​04​]

Find the Inverse of the Matrix (If It Exists) $\left[ \begin{array} { l l } 3 & 0 \\0 & 4\end{array} \right]$