Multiplicative Inverses of Matrices and Matrix Equations
1 Find the Multiplicative Inverse of a Square Matrix
-$$A = \left[ \begin{array} { r r r }
1 & 0 & 0 \
- 5 & 1 & 0 \
0 & 2 & 1
\end{array} \right]$$
A)
$\left[ \begin{array} { r r r } 1 & 0 & 0 \ 5 & 1 & 0 \ - 10 & - 2 & 1 \end{array} \right]$
B)
$\left[ \begin{array} { r r r } 1 & 0 & 0 \ - 5 & 1 & 0 \ 0 & 0 & 2 \end{array} \right]$
C)
$\left[ \begin{array} { r r r } 1 & 2 & 10 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$
D)

$\left[ \begin{array} { r r r } 1 & 0 & 0 \ 2 & - 1 & 0 \ 10 & - 5 & 1 \end{array} \right]$

Question

Multiplicative Inverses of Matrices and Matrix Equations
1 Find the Multiplicative Inverse of a Square Matrix
-$$A = \left[ \begin{array} { r r r } 
1 & 0 & 0 \
- 5 & 1 & 0 \
0 & 2 & 1
\end{array} \right]$$
A)
$\left[ \begin{array} { r r r } 1 & 0 & 0 \ 5 & 1 & 0 \ - 10 & - 2 & 1 \end{array} \right]$
B)
$\left[ \begin{array} { r r r } 1 & 0 & 0 \ - 5 & 1 & 0 \ 0 & 0 & 2 \end{array} \right]$
C)
$\left[ \begin{array} { r r r } 1 & 2 & 10 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{array} \right]$
D)

$\left[ \begin{array} { r r r } 1 & 0 & 0 \ 2 & - 1 & 0 \ 10 & - 5 & 1 \end{array} \right]$

Quizplus · Accepted Answer

The multiplicative inverse of a lower triangular matrix like $A$ can be found by inverting each diagonal element and carefully calculating the off-diagonal elements to maintain the lower triangular form. The correct inverse matrix maintains the structure and inverses the transformation applied by $A$, which in this case is option A.

Multiplicative Inverses of Matrices and Matrix Equations 1 Find the Multiplicative

Multiplicative Inverses of Matrices and Matrix Equations
1 Find the Multiplicative