Find the inverse of A.
$A = \left[ \begin{array} { c c c }
- 4 & 12 & 4 \
8 & 20 & 0 \
12 & 4 & - 8
\end{array} \right]$
A) $A ^ { - 1 } = \frac { 1 } { 36 } \left[ \begin{array} { c c c }
10 & 7 & 5 \
4 & - 1 & 2 \
- 13 & 10 & - 11
\end{array} \right]$
B) $A ^ { - 1 } = \frac { 1 } { 24 } \left[ \begin{array} { c c c }
10 & 7 & 5 \
4 & 1 & 2 \
13 & 10 & 11
\end{array} \right]$
C) $A ^ { - 1 } = \frac { 1 } { 28 } \left[ \begin{array} { c c c }
- 10 & 7 & - 5 \
4 & - 1 & 2 \
- 13 & 10 & - 11
\end{array} \right]$
D) $A ^ { - 1 } = \frac { 1 } { 36 } \left[ \begin{array} { c c c }
- 10 & 7 & - 5 \
4 & - 1 & 2 \
- 13 & 10 & - 11
\end{array} \right]$
E) $A ^ { - 1 } = \frac { 1 } { 28 } \left[ \begin{array} { c c c }
10 & 7 & 5 \
4 & 1 & 2 \
13 & 10 & 11
\end{array} \right]$

Question

Find the inverse of A.
 $A = \left[ \begin{array} { c c c } 
- 4 & 12 & 4 \
8 & 20 & 0 \
12 & 4 & - 8
\end{array} \right]$  
A)  $A ^ { - 1 } = \frac { 1 } { 36 } \left[ \begin{array} { c c c } 
10 & 7 & 5 \
4 & - 1 & 2 \
- 13 & 10 & - 11
\end{array} \right]$
B)  $A ^ { - 1 } = \frac { 1 } { 24 } \left[ \begin{array} { c c c } 
10 & 7 & 5 \
4 & 1 & 2 \
13 & 10 & 11
\end{array} \right]$
C)  $A ^ { - 1 } = \frac { 1 } { 28 } \left[ \begin{array} { c c c } 
- 10 & 7 & - 5 \
4 & - 1 & 2 \
- 13 & 10 & - 11
\end{array} \right]$
D)  $A ^ { - 1 } = \frac { 1 } { 36 } \left[ \begin{array} { c c c } 
- 10 & 7 & - 5 \
4 & - 1 & 2 \
- 13 & 10 & - 11
\end{array} \right]$
E)  $A ^ { - 1 } = \frac { 1 } { 28 } \left[ \begin{array} { c c c } 
10 & 7 & 5 \
4 & 1 & 2 \
13 & 10 & 11
\end{array} \right]$

Quizplus · Accepted Answer

The inverse of matrix A is calculated using the formula for the inverse of a 3x3 matrix. After computing the determinant and the adjugate matrix, the correct inverse is option D.

Find the Inverse of A A=[−41248200124−8]A = \left[ \begin{array} { c c c } - 4 & 12 & 4 \\8 & 20 & 0 \\12 & 4 & - 8\end{array} \right]A=​−4812​12204​40−8​​

Find the Inverse of A $A = \left[ \begin{array} { c c c } - 4 & 12 & 4 \\8 & 20 & 0 \\12 & 4 & - 8\end{array} \right]$