Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { r r }
2 & 8 \
3 & 12
\end{array} \right]$$
A)
$$\left[ \begin{array} { r r }
12 & - 8 \
- 5 & 3
\end{array} \right]$$
B) Inverse does not exist
C)
$$\left[ \begin{array} { r r }
12 & - 8 \
- 3 & 2
\end{array} \right]$$
D)
$$\left[ \begin{array} { c c }
\frac { 1 } { 2 } & 0 \
0 & \frac { 1 } { 12 }
\end{array} \right]$$

Question

Find the inverse of A if it has one, or state that the inverse does not exist.
-$$A = \left[ \begin{array} { r r } 
2 & 8 \
3 & 12
\end{array} \right]$$
A)
$$\left[ \begin{array} { r r } 
12 & - 8 \
- 5 & 3
\end{array} \right]$$
B) Inverse does not exist
C)
$$\left[ \begin{array} { r r } 
12 & - 8 \
- 3 & 2
\end{array} \right]$$
D)
$$\left[ \begin{array} { c c } 
\frac { 1 } { 2 } & 0 \
0 & \frac { 1 } { 12 }
\end{array} \right]$$

Quizplus · Accepted Answer

The determinant of matrix A is $2(12) - 8(3) = 24 - 24 = 0$. A matrix has an inverse if and only if its determinant is non-zero. Since the determinant is 0, the inverse does not exist.

Find the Inverse of a If It Has One, or State