If (P = begin{vmatrix} 1 & 1 \ 2 & 1 end{vmatrix}), find ((P^{2} + P)).
- A.
(begin{vmatrix} 4 & 3 \ 6 & 1 end{vmatrix}) - B.
(begin{vmatrix} 4 & 3 \ 6 & 4 end{vmatrix}) - C.
(begin{vmatrix} 2 & 2 \ 6 & 2 end{vmatrix}) - D.
(begin{vmatrix} 3 & 2 \ 6 & 4 end{vmatrix})
Correct Answer: Option B
Explanation
( P^{2} = begin{vmatrix} 1 & 1 \ 2 & 1 end{vmatrix} begin{vmatrix} 1 & 1 \ 2 & 1 end{vmatrix})
(begin{vmatrix} 1 times 1 + 1 times 2 & 1 times 1 + 1 times 1 \ 2 times 1 + 1 times 2 & 2 times 1 + 1 times 1 end{vmatrix})
= (begin{vmatrix} 3 & 2 \ 4 & 3 end{vmatrix} + begin{vmatrix} 1 & 1 \ 2 & 1 end{vmatrix})
= (begin{vmatrix} 4 & 3 \ 6 & 4 end{vmatrix})