If (P = begin{pmatrix} 1 & -2 \ 3 & 4 end{pmatrix}) and (Q = begin{pmatrix} -2 & 3 \ 1 & 0 end{pmatrix}), find PQ.
-
A.
(begin{pmatrix} 4 & 1 \ -2 & 9 end{pmatrix}) -
B.
(begin{pmatrix} -4 & 1 \ 2 & 9 end{pmatrix}) -
C.
(begin{pmatrix} -4 & 3 \ -2 & 13 end{pmatrix}) -
D.
(begin{pmatrix} -4 & 3 \ -2 & 9 end{pmatrix})
Correct Answer: Option D
Explanation
(begin{pmatrix} 1 & -2 \ 3 & 4 end{pmatrix} (begin{pmatrix} -2 & 3 \ 1 & 0 end{pmatrix})
= (begin{pmatrix} (1 times -2) + (-2 times 1) & (1 times 3) + (-2 times 0) \ (3 times -2) + (4 times 1) & (3 times 3) + (4 times 0) end{pmatrix})
= (begin{pmatrix} -4 & 3 \ -2 & 9 end{pmatrix})