Match List-I with List-II

Choose the correct answer from the options given below:

(A)-(I), (B)-(IV), (C)-(II), (D)-(III)

The correct answer is Option (3) → (A)-(I), (B)-(IV), (C)-(II), (D)-(III)

(A) $[a_{ij}]_{2\times 2} \times [b_{ij}]_{2\times 4}$

Inner dimensions: 2 and 2 → possible → result is $2\times 4$

Matches (I)

(B) $[a_{ij}]_{2\times 1} \times [b_{ij}]_{1\times 3}$

Inner dimensions: 1 and 1 → possible → result is $2\times 3$

Matches (IV)

(C) $[a_{ij}]_{3\times 2} \times [b_{ij}]_{3\times 2}$

Inner dimensions: 2 and 3 → not equal → not possible

Matches (II)

(D) $[a_{ij}]_{3\times 3} \times [b_{ij}]_{3\times 3}$

Inner dimensions: 3 and 3 → possible → result is $3\times 3$

Matches (III)

The correct matching is: A–I, B–IV, C–II, D–III.