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

Question

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

Quizplus · Accepted Answer

To find the inverse of a matrix, we can use the method of Gauss-Jordan elimination or the formula for the inverse of a 3x3 matrix. However, for this specific matrix, we can directly verify the answer by multiplying the given matrix by each of the options. The correct inverse matrix, when multiplied by the original matrix, will yield the identity matrix. Option A is the correct inverse because when it is multiplied by the given matrix, it results in the identity matrix $\left[ \begin{array} { r r r } 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array} \right]$, which confirms it is the inverse.

Find the Inverse of the Matrix [100−110111]\left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\1 & 1 & 1\end{array} \right]​1−11​011​001​​

Find the Inverse of the Matrix $\left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\1 & 1 & 1\end{array} \right]$