Let \(A = [a_{ij}]_{3 \times 2}\) and \(B = [b_{ij}]_{3 \times 4}\) be two matrices. Then the order of the matrix \((A^T. B)^T\) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 × 2
The transpose swaps the order, and a product of an \(m \times n\) and an \(n \times p\) matrix has order m × p.
\(A^T\): \(2 \times 3\)
\(A^T B\): \((2 \times 3)(3 \times 4) = 2 \times 4\)
\((A^T B)^T\): \(4 \times 2\)