A and B are two matrices such that the order of A is $3 \times 4$, if $A'B$ and $BA'$ are both defined, then
Step-by-Step Solution
Key Concept: For matrix multiplication $PQ$ to be defined, the number of columns in $P$ must equal the number of rows in $Q$.
Since $A$ is $4 imes 4$, the transpose $A'$ is also $4 imes 4$. For the product $A'B$ to be defined, the number of columns in $A'$ must equal the number of rows in $B$. Therefore, $m = 4$. Since no constraint is given on $n$, and the problem asks for the order when $A'B$ is defined, the order of $B$ is $4 imes 4$.
Correct Answer: 4×4