Find the inverse of the invertible matrix.
-$$\left[ \begin{array} { r r r }
3 & - 3 & 1 \
- 2 & 2 & - 1 \
- 4 & 5 & - 2
\end{array} \right]$$
A) $\left[ \begin{array} { r r r } 1 & - 1 & 1 \ - 2 & - 3 & 0 \ 0 & - 2 & 1 \end{array} \right]$
B) $\left[ \begin{array} { r r r } 1 & - 3 & 1 \ 0 & - 2 & 1 \ - 2 & - 3 & 0 \end{array} \right]$
C) $\left[ \begin{array} { r r r } 1 & - 1 & 0 \ - 2 & - 3 & 0 \ 0 & - 2 & - 1 \end{array} \right]$
D) $\left[ \begin{array} { r r r } 1 & - 1 & 1 \ 0 & - 2 & 1 \ - 2 & - 3 & 0 \end{array} \right]$

Question

Find the inverse of the invertible matrix.
-$$\left[ \begin{array} { r r r } 
3 & - 3 & 1 \
- 2 & 2 & - 1 \
- 4 & 5 & - 2
\end{array} \right]$$
A) $\left[ \begin{array} { r r r } 1 & - 1 & 1 \ - 2 & - 3 & 0 \ 0 & - 2 & 1 \end{array} \right]$
B) $\left[ \begin{array} { r r r } 1 & - 3 & 1 \ 0 & - 2 & 1 \ - 2 & - 3 & 0 \end{array} \right]$
C) $\left[ \begin{array} { r r r } 1 & - 1 & 0 \ - 2 & - 3 & 0 \ 0 & - 2 & - 1 \end{array} \right]$
D) $\left[ \begin{array} { r r r } 1 & - 1 & 1 \ 0 & - 2 & 1 \ - 2 & - 3 & 0 \end{array} \right]$

Quizplus · Accepted Answer

To find the inverse of the given matrix, one would typically use the method involving finding the matrix of cofactors, transposing that matrix to get the adjugate, and then dividing by the determinant of the original matrix. Without performing these calculations explicitly here, the correct answer can be verified through direct calculation or by using a matrix calculator to confirm that option D is indeed the inverse of the given matrix.

Find the Inverse of the Invertible Matrix [3−31−22−1−45−2]\left[ \begin{array} { r r r } 3 & - 3 & 1 \\- 2 & 2 & - 1 \\- 4 & 5 & - 2\end{array} \right]​3−2−4​−325​1−1−2​​

Find the Inverse of the Invertible Matrix $\left[ \begin{array} { r r r } 3 & - 3 & 1 \\- 2 & 2 & - 1 \\- 4 & 5 & - 2\end{array} \right]$