Find the inverse of the matrix $\left[ \begin{array} { c c c }
8 & 8 & 8 \
24 & 40 & 32 \
24 & 48 & 40
\end{array} \right]$ .
A) $\frac { 1 } { 8 } \left[ \begin{array} { c c c }
1 & 1 & - 1 \
- 3 & 2 & - 1 \
3 & - 3 & 2
\end{array} \right]$
B) $\frac { 1 } { 8 } \left[ \begin{array} { c c c }
- 1 & 1 & 1 \
0 & - 2 & - 1 \
3 & - 3 & 2
\end{array} \right]$
C) $8 \left[ \begin{array} { c c c }
1 & 1 & - 1 \
- 3 & 0 & - 1 \
3 & - 3 & 2
\end{array} \right]$
D) $- \frac { 1 } { 8 } \left[ \begin{array} { c c c }
1 & 0 & - 1 \
- 3 & 2 & - 1 \
2 & - 3 & 3
\end{array} \right]$
E) $- 8 \left[ \begin{array} { c c c }
3 & 1 & 0 \
- 3 & 1 & - 1 \
1 & - 3 & 2
\end{array} \right]$

Question

Find the inverse of the matrix $\left[ \begin{array} { c c c } 
8 & 8 & 8 \
24 & 40 & 32 \
24 & 48 & 40
\end{array} \right]$ .
A) $\frac { 1 } { 8 } \left[ \begin{array} { c c c } 
1 & 1 & - 1 \
- 3 & 2 & - 1 \
3 & - 3 & 2
\end{array} \right]$
B) $\frac { 1 } { 8 } \left[ \begin{array} { c c c } 
- 1 & 1 & 1 \
0 & - 2 & - 1 \
3 & - 3 & 2
\end{array} \right]$
C) $8 \left[ \begin{array} { c c c } 
1 & 1 & - 1 \
- 3 & 0 & - 1 \
3 & - 3 & 2
\end{array} \right]$
D) $- \frac { 1 } { 8 } \left[ \begin{array} { c c c } 
1 & 0 & - 1 \
- 3 & 2 & - 1 \
2 & - 3 & 3
\end{array} \right]$
E) $- 8 \left[ \begin{array} { c c c } 
3 & 1 & 0 \
- 3 & 1 & - 1 \
1 & - 3 & 2
\end{array} \right]$

Quizplus · Accepted Answer

To find the inverse of a matrix, one typically uses the formula $A^{-1} = \frac{1}{\text{det}(A)} \cdot \text{adj}(A)$, where $\text{det}(A)$ is the determinant of the matrix $A$ and $\text{adj}(A)$ is the adjugate of $A$. The given matrix's inverse matches option A when calculated correctly, taking into account the determinant and the cofactors for each element in the matrix.

Find the Inverse of the Matrix [888244032244840]\left[ \begin{array} { c c c } 8 & 8 & 8 \\24 & 40 & 32 \\24 & 48 & 40\end{array} \right]​82424​84048​83240​​

Find the Inverse of the Matrix $\left[ \begin{array} { c c c } 8 & 8 & 8 \\24 & 40 & 32 \\24 & 48 & 40\end{array} \right]$