Multiplicative Inverses of Matrices and Matrix Equations
1 Find the Multiplicative Inverse of a Square Matrix
-$$\mathrm { A } = \left[ \begin{array} { r r r r }
1 & 6 & 0 & 0 \
0 & 1 & - 1 & 0 \
0 & 0 & 1 & - 8 \
0 & 0 & 0 & 1
\end{array} \right]$$

A)
$$\left[ \begin{array} { r r r c }
1 & - 6 & - 6 & - 48 \
0 & 1 & 1 & 8 \
0 & 0 & 1 & 8 \
0 & 0 & 0 & 1
\end{array} \right]$$
B)$$\left[ \begin{array} { r r r r }
1 & 8 & - 8 & - 48 \
0 & 1 & 1 & 6 \
0 & 0 & 1 & - 6 \
0 & 0 & 0 & 1
\end{array} \right]$$

C)
$$\left[ \begin{array} { r r r r }
1 & 0 & 0 & 0 \
8 & 1 & 0 & 0 \
- 8 & 1 & 1 & 0 \
- 48 & 6 & - 6 & 1
\end{array} \right]$$
D)
$$\left[ \begin{array} { r r r r }
1 & 0 & 0 & 0 \
- 6 & 1 & 0 & 0 \
- 6 & 1 & 1 & 0 \
- 48 & 8 & 8 & 1
\end{array} \right]$$

Question

Multiplicative Inverses of Matrices and Matrix Equations
1 Find the Multiplicative Inverse of a Square Matrix
-$$\mathrm { A } = \left[ \begin{array} { r r r r } 
1 & 6 & 0 & 0 \
0 & 1 & - 1 & 0 \
0 & 0 & 1 & - 8 \
0 & 0 & 0 & 1
\end{array} \right]$$

A)
$$\left[ \begin{array} { r r r c } 
1 & - 6 & - 6 & - 48 \
0 & 1 & 1 & 8 \
0 & 0 & 1 & 8 \
0 & 0 & 0 & 1
\end{array} \right]$$
B)$$\left[ \begin{array} { r r r r } 
1 & 8 & - 8 & - 48 \
0 & 1 & 1 & 6 \
0 & 0 & 1 & - 6 \
0 & 0 & 0 & 1
\end{array} \right]$$

C)
$$\left[ \begin{array} { r r r r } 
1 & 0 & 0 & 0 \
8 & 1 & 0 & 0 \
- 8 & 1 & 1 & 0 \
- 48 & 6 & - 6 & 1
\end{array} \right]$$
D)
$$\left[ \begin{array} { r r r r } 
1 & 0 & 0 & 0 \
- 6 & 1 & 0 & 0 \
- 6 & 1 & 1 & 0 \
- 48 & 8 & 8 & 1
\end{array} \right]$$

Quizplus · Accepted Answer

The multiplicative inverse of a square matrix A is found by applying row operations to transform A into the identity matrix, while simultaneously applying the same operations to the identity matrix. The resulting matrix is the inverse of A. For the given matrix A, its structure suggests that it is an upper triangular matrix with ones along the diagonal, indicating it is invertible. The correct inverse matrix systematically undoes the effects of A, which involves subtracting multiples of the rows from each other in reverse order from how they were added in A. Option A correctly performs these operations, yielding the inverse that, when multiplied by A, would result 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