Multiplicative Inverses of Matrices and Matrix Equations
1 Find the Multiplicative Inverse of a Square Matrix
-$$\mathrm { A } = \left[ \begin{array} { r r r }
1 & 0 & 0 \
- 1 & 1 & 0 \
1 & 1 & 1
\end{array} \right]$$
A)
$$\left[ \begin{array} { r r r }
1 & 0 & 0 \
1 & 1 & 0 \
- 2 & - 1 & 1
\end{array} \right]$$
B)
$\left[ \begin{array} { l l l } 1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$
C)
$\left[ \begin{array} { r r r } 1 & - 1 & 1 \ 0 & 1 & - 1 \ 0 & 0 & 1 \end{array} \right]$
D)
$\left[ \begin{array} { r r r } - 1 & 0 & 0 \ - 1 & - 1 & 0 \ - 1 & - 1 & - 1 \end{array} \right]$

Question

Multiplicative Inverses of Matrices and Matrix Equations
1 Find the Multiplicative Inverse of a Square Matrix
-$$\mathrm { A } = \left[ \begin{array} { r r r } 
1 & 0 & 0 \
- 1 & 1 & 0 \
1 & 1 & 1
\end{array} \right]$$
A)
$$\left[ \begin{array} { r r r } 
1 & 0 & 0 \
1 & 1 & 0 \
- 2 & - 1 & 1
\end{array} \right]$$
B)
$\left[ \begin{array} { l l l } 1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$
C)
$\left[ \begin{array} { r r r } 1 & - 1 & 1 \ 0 & 1 & - 1 \ 0 & 0 & 1 \end{array} \right]$
D)
$\left[ \begin{array} { r r r } - 1 & 0 & 0 \ - 1 & - 1 & 0 \ - 1 & - 1 & - 1 \end{array} \right]$

Quizplus · Accepted Answer

The multiplicative inverse of a matrix $A$ is the matrix that, when multiplied with $A$, yields the identity matrix. The given matrix $A$ is upper triangular, and its inverse can be calculated directly or through methods such as Gaussian elimination. Option A is the correct inverse because when multiplied with the original matrix $A$, it results in the identity matrix.

Multiplicative Inverses of Matrices and Matrix Equations 1 Find the Multiplicative

Multiplicative Inverses of Matrices and Matrix Equations
1 Find the Multiplicative