Let \(A = \begin{bmatrix}1&-1&2\\0&3&1\end{bmatrix}\) and \(B = \begin{bmatrix}2&1\\1&0\\-1&4\end{bmatrix}\).
Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (A) | Element in the first row, second column of AB | (I) | 4 |
| (B) | Element in the second row, second column of AB | (II) | 9 |
| (C) | Element in the first row, third column of BA | (III) | \(-1\) |
| (D) | Element in the third row, first column of BA | (IV) | 5 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
The element in row i, column j of a product is row i of the first matrix times column j of the second. AB is of order \(2 \times 2\) and BA is of order \(3 \times 3\).
(A) Element in the first row, second column of AB
This matches (II) 9.
\(1(1) + (-1)(0) + 2(4) = 9\)
(B) Element in the second row, second column of AB
This matches (I) 4.
\(0(1) + 3(0) + 1(4) = 4\)
(C) Element in the first row, third column of BA
This matches (IV) 5.
\(2(2) + 1(1) = 5\)
(D) Element in the third row, first column of BA
This matches (III) \(-1\).
\((-1)(1) + 4(0) = -1\)