Three shopkeepers A, B, C go to store to buy stationary. A purchases 10 dozen pens, 6 dozen pencils. B purchases 10 dozen notebooks, 5 dozen pens and 7 dozen pencils. C purchases 11 dozen notebooks and 13 dozen pens. A notebook costs 40 paise, a pen costs 1.25 rupees and pencil costs 35 paise. Identity correct statements:

(A) If P is quantity matrix (stationary purchased by A, B, C) then order of P is $2×3$

(B) If Q is a price matrix then order of matrix Q is $(3×1)$, to get individual bills

(C)  Q is $\begin{bmatrix} 0 & 10 & 6\\10 & 5 & 7\\11 & 13 & 0 \end{bmatrix}$

(D) Q is [0.40   1.25   0.35 ]

(E) Matrix P  is $ \begin{pmatrix}0& 120& 72\\120 & 60& 84\\132 & 156 & 0 \end{pmatrix}$

Choose the correct answer from the options given below :

(B), (E) Only

The correct answer is Option (4) → (B) Only

Let pens be $x$, pencil be $y$ and notebooks be $z$.

$A → 10x+6y$

$B → 5x+7y+11z$

$C → 13x+11z$

$⇒P=\begin{bmatrix}10&6&0\\5&7&11\\13&0&11\end{bmatrix}_{3×3}$

$Q=\begin{bmatrix}0.35\\1.25\\0.40\end{bmatrix}_{3×1}$

∴ Q is of order 3×1.