If \(A = \begin{pmatrix} 1 & -2 & 3\\ -4 & 2 & 5\end{pmatrix}\) and \(B = \begin{pmatrix} 2 & 3\\ 4 & 5\\ 2 & 1\end{pmatrix}\) and \(BA = (b_{ij})\), then \(b_{21} + b_{32} =\)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → −18
B is of order 3 × 2 and A of order 2 × 3, so BA is a 3 × 3 matrix. Its entry \(b_{ij}\) is row i of B times column j of A; only the two required entries are needed.
\(b_{21}\): row 2 of B is (4, 5), column 1 of A is (1, −4):
\(b_{21} = 4(1) + 5(-4) = 4 - 20 = -16\)
\(b_{32}\): row 3 of B is (2, 1), column 2 of A is (−2, 2):
\(b_{32} = 2(-2) + 1(2) = -4 + 2 = -2\)
Adding:
\(b_{21} + b_{32} = -16 + (-2) = -18\)