Let A, B and C be matrices of orders \(2 \times 3\), \(3 \times 2\) and \(2 \times 2\) respectively.
Match List-I with List-II
| List-I (Matrix) | List-II (Order) | ||
|---|---|---|---|
| (A) | AB | (I) | \(2 \times 3\) |
| (B) | BA | (II) | \(3 \times 3\) |
| (C) | \(A'C\) | (III) | \(2 \times 2\) |
| (D) | CA | (IV) | \(3 \times 2\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
The product of an \(m \times n\) matrix and an \(n \times p\) matrix is defined and has order \(m \times p\): rows of the first, columns of the second.
(A) AB
This matches (III) \(2 \times 2\).
\((2 \times 3)(3 \times 2) \rightarrow 2 \times 2\)
(B) BA
This matches (II) \(3 \times 3\).
\((3 \times 2)(2 \times 3) \rightarrow 3 \times 3\)
(C) \(A'C\)
This matches (IV) \(3 \times 2\). The transpose \(A'\) has order \(3 \times 2\).
\((3 \times 2)(2 \times 2) \rightarrow 3 \times 2\)
(D) CA
This matches (I) \(2 \times 3\).
\((2 \times 2)(2 \times 3) \rightarrow 2 \times 3\)