Find the products AB and BA to determine whether B is the multiplicative inverse of A.
-$$A = \left[ \begin{array} { r r }
4 & - 2 \
- 6 & 2
\end{array} \right]$$
A)
$$\left[ \begin{array} { l }
- \frac { 1 } { 2 } - \frac { 1 } { 2 } \
- \frac { 3 } { 2 } - 1
\end{array} \right]$$
B)
$$\left[ \begin{array} { r r }
- \frac { 1 } { 2 } & \frac { 1 } { 2 } \
\frac { 3 } { 2 } & - 1
\end{array} \right]$$
C)
$$\left[ \begin{array} { l }
- \frac { 3 } { 2 } - 1 \
- \frac { 1 } { 2 } - \frac { 1 } { 2 }
\end{array} \right]$$
D)

$$\left[ \begin{array} { c }
- 1 - \frac { 1 } { 2 } \
- \frac { 3 } { 2 } - \frac { 1 } { 2 }
\end{array} \right]$$

Question

Find the products AB and BA to determine whether B is the multiplicative inverse of A.
-$$A = \left[ \begin{array} { r r } 
4 & - 2 \
- 6 & 2
\end{array} \right]$$
A)
$$\left[ \begin{array} { l } 
- \frac { 1 } { 2 } - \frac { 1 } { 2 } \
- \frac { 3 } { 2 } - 1
\end{array} \right]$$
B)
$$\left[ \begin{array} { r r } 
- \frac { 1 } { 2 } & \frac { 1 } { 2 } \
\frac { 3 } { 2 } & - 1
\end{array} \right]$$
C)
$$\left[ \begin{array} { l } 
- \frac { 3 } { 2 } - 1 \
- \frac { 1 } { 2 } - \frac { 1 } { 2 }
\end{array} \right]$$
D)

$$\left[ \begin{array} { c } 
- 1 - \frac { 1 } { 2 } \
- \frac { 3 } { 2 } - \frac { 1 } { 2 }
\end{array} \right]$$

Quizplus · Accepted Answer

Explanation:The multiplicative inverse of a matrix A is a matrix B such that AB = BA = I, where I is the identity matrix.To find the multiplicative inverse of A, we can use the formula B = A^-1, where A^-1 is the inverse of A.To find the inverse of A, we can use the formula A^-1 = (1/det(A)) * C^T, where det(A) is the determinant of A and C^T is the transpose of the cofactor matrix of A.The determinant of A is det(A) = (4 * 2) - (-6 * -2) = 8 - 12 = -4.The cofactor matrix of A is C = [2 2; 6 4].The transpose of the cofactor matrix of A is C^T = [2 6; 2 4].Therefore, the inverse of A is A^-1 = (1/-4) * [2 6; 2 4] = [-1/2 -3/2; -1/2 -1].Therefore, the multiplicative inverse of A is B = [-1/2 -3/2; -1/2 -1].To check if B is the multiplicative inverse of A, we can calculate AB and BA.AB = [-1/2 -3/2; -1/2 -1] * [4 -2; -6 2] = [1 0; 0 1].BA = [4 -2; -6 2] * [-1/2 -3/2; -1/2 -1] = [1 0; 0 1].Therefore, AB = BA = I, which means that B is the multiplicative inverse of A.

Find the Products AB and BA to Determine Whether B A=[4−2−62]A = \left[ \begin{array} { r r } 4 & - 2 \\- 6 & 2\end{array} \right]A=[4−6​−22​]

Find the Products AB and BA to Determine Whether B $A = \left[ \begin{array} { r r } 4 & - 2 \\- 6 & 2\end{array} \right]$