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:
Answer & explanation
Correct answer: option 1
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).