Match List-I with List-II
| List-I | List-II | ||
| Matrix Product | Order of resultant matrix | ||
| (A) | \([a_{ij}]_{2 \times 3} \times [b_{ij}]_{3 \times 4}\) | (I) | \(2 \times 4\) |
| (B) | \([a_{ij}]_{2 \times 1} \times [b_{ij}]_{1 \times 3}\) | (II) | Not possible |
| (C) | \([a_{ij}]_{3 \times 2} \times [b_{ij}]_{3 \times 2}\) | (III) | \(3 \times 3\) |
| (D) | \([a_{ij}]_{3 \times 3} \times [b_{ij}]_{3 \times 3}\) | (IV) | \(2 \times 3\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(I), (B)-(IV), (C)-(II), (D)-(III)
The product of an \(m \times n\) matrix and a \(p \times q\) matrix is defined only when the inner orders are equal (\(n = p\)), and then the product has order \(m \times q\).
(A) \([a_{ij}]_{2 \times 3} \times [b_{ij}]_{3 \times 4}\)
This matches (I) \(2 \times 4\): the inner orders are 3 and 3, so the product is \(2 \times 4\).
(B) \([a_{ij}]_{2 \times 1} \times [b_{ij}]_{1 \times 3}\)
This matches (IV) \(2 \times 3\): the inner orders are 1 and 1, so the product is \(2 \times 3\).
(C) \([a_{ij}]_{3 \times 2} \times [b_{ij}]_{3 \times 2}\)
This matches (II) Not possible: the inner orders are 2 and 3, which are not equal.
(D) \([a_{ij}]_{3 \times 3} \times [b_{ij}]_{3 \times 3}\)
This matches (III) \(3 \times 3\): the inner orders are 3 and 3, so the product is \(3 \times 3\).
So the matching is (A)-(I), (B)-(IV), (C)-(II), (D)-(III).
NCERT (2026-27 edition):
Operations on Matrices
