Find the products AB and BA to determine whether B is the multiplicative inverse of A.
-$$A = \left[ \begin{array} { r r r }
1 & 0 & 0 \
- 1 & 1 & 0 \
0 & - 6 & 1
\end{array} \right]$$
A)
$\left[ \begin{array} { l l l } 1 & 0 & 0 \ 1 & 1 & 0 \ 6 & 6 & 1 \end{array} \right]$
B)

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

D)
$\left[\begin{array}{rrr}
1 & 0 & 0 \
-6 & -1 & 0 \
-6 & -1 & 1
\end{array}\right]$

Question

Find the products AB and BA to determine whether B is the multiplicative inverse of A.
-$$A = \left[ \begin{array} { r r r } 
1 & 0 & 0 \
- 1 & 1 & 0 \
0 & - 6 & 1
\end{array} \right]$$
A)
$\left[ \begin{array} { l l l } 1 & 0 & 0 \ 1 & 1 & 0 \ 6 & 6 & 1 \end{array} \right]$
B)

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

D)
$\left[\begin{array}{rrr}
1 & 0 & 0 \
-6 & -1 & 0 \
-6 & -1 & 1
\end{array}\right]$

Quizplus · Accepted Answer

Matrix B is the multiplicative inverse of A if and only if AB = BA = I, where I is the identity matrix. The given matrix A is an upper triangular matrix with ones on the diagonal, which suggests that its inverse would also be an upper triangular matrix with ones on the diagonal. The correct choice, A, is the only matrix that, when multiplied by A from either side, would result in the identity matrix, confirming it as the multiplicative inverse of A.

Find the Products AB and BA to Determine Whether B A=[100−1100−61]A = \left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\0 & - 6 & 1\end{array} \right]A=​1−10​01−6​001​​

Find the Products AB and BA to Determine Whether B $A = \left[ \begin{array} { r r r } 1 & 0 & 0 \\- 1 & 1 & 0 \\0 & - 6 & 1\end{array} \right]$