Let A, B and C be matrices of orders \(2 \times 3\), \(3 \times 4\) and \(4 \times 2\) respectively.
Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| Matrix | Order | ||
| (A) | \(AB\) | (I) | \(3 \times 2\) |
| (B) | \(CA\) | (II) | \(2 \times 4\) |
| (C) | \(B^{T}A^{T}\) | (III) | \(4 \times 3\) |
| (D) | \(BC\) | (IV) | \(4 \times 2\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(III), (C)-(IV), (D)-(I)
A product PQ is defined when the number of columns of P equals the number of rows of Q. Then
\((m \times n)(n \times p) \text{ gives } m \times p\)
A transpose swaps rows and columns: \(A^{T}\) is \(3 \times 2\) and \(B^{T}\) is \(4 \times 3\).
(A) \(AB\)
This matches (II) \(2 \times 4\):
\((2 \times 3)(3 \times 4) \text{ gives } 2 \times 4\)
(B) \(CA\)
This matches (III) \(4 \times 3\):
\((4 \times 2)(2 \times 3) \text{ gives } 4 \times 3\)
(C) \(B^{T}A^{T}\)
This matches (IV) \(4 \times 2\):
\((4 \times 3)(3 \times 2) \text{ gives } 4 \times 2\)
This agrees with \(B^{T}A^{T} = (AB)^{T}\), the transpose of a \(2 \times 4\) matrix.
(D) \(BC\)
This matches (I) \(3 \times 2\):
\((3 \times 4)(4 \times 2) \text{ gives } 3 \times 2\)