Find the inverse matrix of A.
-$$A = \left[ \begin{array} { l l l }
1 & 1 & 1 \
2 & 1 & 1 \
2 & 2 & 3
\end{array} \right]$$
A) $\left[ \begin{array} { r r r } - 1 & 1 & 0 \ 4 & - 1 & - 1 \ - 2 & 0 & 1 \end{array} \right]$
B) $\left[ \begin{array} { c c c } 1 & 1 & 1 \ \frac { 1 } { 2 } & 1 & 1 \ \frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 } \end{array} \right]$
C) $\left[ \begin{array} { l l l } - 1 & - 1 & - 1 \ - 2 & - 1 & - 1 \ - 2 & - 2 & - 3 \end{array} \right]$
D) $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$

Question

Find the inverse matrix of A.
-$$A = \left[ \begin{array} { l l l } 
1 & 1 & 1 \
2 & 1 & 1 \
2 & 2 & 3
\end{array} \right]$$
A) $\left[ \begin{array} { r r r } - 1 & 1 & 0 \ 4 & - 1 & - 1 \ - 2 & 0 & 1 \end{array} \right]$
B) $\left[ \begin{array} { c c c } 1 & 1 & 1 \ \frac { 1 } { 2 } & 1 & 1 \ \frac { 1 } { 2 } & \frac { 1 } { 2 } & \frac { 1 } { 3 } \end{array} \right]$
C) $\left[ \begin{array} { l l l } - 1 & - 1 & - 1 \ - 2 & - 1 & - 1 \ - 2 & - 2 & - 3 \end{array} \right]$
D) $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$

Quizplus · Accepted Answer

The inverse of matrix A can be found using the formula $A^{-1} = \frac{1}{\text{det}(A)} \text{adj}(A)$, where $\text{det}(A)$ is the determinant of A and $\text{adj}(A)$ is the adjugate of A. Calculating the determinant and the adjugate of A and then applying the formula yields the matrix in choice A as the correct inverse.

Find the Inverse Matrix of A A=[111211223]A = \left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]A=​122​112​113​​

Find the Inverse Matrix of A $A = \left[ \begin{array} { l l l } 1 & 1 & 1 \\2 & 1 & 1 \\2 & 2 & 3\end{array} \right]$