If P, Q and R are matrices of order 2 × 3, 3 × 5 and 5 × 3 respectively. Then which of the following are valid?

(A) P Q R
(B) P R Q
(C) Q R
(D) R Q
(E) P R

Choose the correct answer from the options given below:

(A), (C) and (D) only

The correct answer is Option (1) → (A), (C) and (D) only

Order of $P$ is $2\times3$

Order of $Q$ is $3\times5$

Order of $R$ is $5\times3$

(A) $PQR$

$P(2\times3)\cdot Q(3\times5)$ is valid and gives $2\times5$

$(2\times5)\cdot R(5\times3)$ is valid and gives $2\times3$

Valid

(B) $PRQ$

$P(2\times3)\cdot R(5\times3)$ is not valid since $3\ne5$

Not valid

(C) $QR$

$Q(3\times5)\cdot R(5\times3)$ is valid and gives $3\times3$

Valid

(D) $RQ$

$R(5\times3)\cdot Q(3\times5)$ is valid and gives $5\times5$

Valid

(E) $PR$

$P(2\times3)\cdot R(5\times3)$ is not valid since $3\ne5$

Not valid

The valid products are (A), (C) and (D).