If A is a m × n matrix and B is n × p matrix and m ≠ p then,

$(AB)^T= B^TA^T$

Given $A$ is an $m\times n$ matrix and $B$ is an $n\times p$ matrix.

The product $AB$ is defined and is of order $m\times p$.

Property of transpose:

$(AB)^T = B^T A^T$ always holds, irrespective of $m\neq p$.

Check options:

Option 1: $(AB)^T = B^T A^T$ → correct.

Option 2: $(BA)' = A'B'$ → $BA$ may not even be defined, so incorrect.

Option 3: $(AB)' = A'B'$ → incorrect order.

Option 4: $(BA)' = B'A'$ → $BA$ may not be defined.

final answer: Option 1