Let $B = \left[ \begin{array} { l l } - & 3 \ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 4 & 1 \end{array} \right]$.
Perform the operation: $( B C ) ^ { 2 }$.
A)
$\left[ \begin{array} { l } - 80 \ - 20 \end{array} \right]$

B) $[ 120 ]$

C) $\left[ \begin{array} { r r } 120 & 30 \ - 80 & - 20 \end{array} \right]$

D) $\left[ \begin{array} { l l } 120 & 30 \end{array} \right]$

E) none of these

Question

Let $B = \left[ \begin{array} { l l } - & 3 \ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 4 & 1 \end{array} \right]$.
Perform the operation: $( B C ) ^ { 2 }$.
A)
$\left[ \begin{array} { l } - 80 \ - 20 \end{array} \right]$

B) $[ 120 ]$

C) $\left[ \begin{array} { r r } 120 & 30 \ - 80 & - 20 \end{array} \right]$

D) $\left[ \begin{array} { l l } 120 & 30 \end{array} \right]$

E) none of these

Quizplus · Accepted Answer

First, we perform the matrix multiplication of B and C:
$$BC = \left[ \begin{array} { l l } - & 3 \ 2 \end{array} ight] \left[ \begin{array} { l l } 4 & 1 \end{array} ight] = \left[ \begin{array} { r r } -12 & -3 \ 8 & 2 \end{array} ight]$$
Then, we compute the square of BC:
$$(BC)^2 = \left[ \begin{array} { r r } -12 & -3 \ 8 & 2 \end{array} ight] \left[ \begin{array} { r r } -12 & -3 \ 8 & 2 \end{array} ight] = \left[ \begin{array} { r r } 120 & 30 \ -80 & -20 \end{array} ight]$$
Therefore, the answer is choice C.

Let B=[−32],C=[41]B = \left[ \begin{array} { l l } - & 3 \\ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 4 & 1 \end{array} \right]B=[−2​3],C=[4​1​]

Let $B = \left[ \begin{array} { l l } - & 3 \\ 2 \end{array} \right] , C = \left[ \begin{array} { l l } 4 & 1 \end{array} \right]$