If A is a matrix of order \(m \times n\) and B is another matrix such that \(A'B\) and \(BA'\) are both defined, then the order of matrix B is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(m \times n\)
Since A is of order \(m \times n\), its transpose A′ is of order \(n \times m\). Let B be of order \(p \times q\).
A product PQ is defined only when the number of columns of P equals the number of rows of Q.
A′B is defined: A′ has m columns, so B has m rows:
\(p = m\)
BA′ is defined: A′ has n rows, so B has n columns:
\(q = n\)
Hence B is of order \(m \times n\).