Question:
If $A$ is a matrix of order $m \times n$ and $B$ is a matrix such that $A B^{T}$ and $B^{T} A$ are both defined, then the order of matrix $B$ is
(a) $m \times n$
(b) $n \times n$
(c) $n \times m$
(d) $m \times n$
Disclaimer: option (a) and (d) both are the same.
Solution:
Since, $A B^{T}$ and $B^{T} A$ are both defined.
And, order of $A$ is $m \times n .$ So, Order of $B^{T}$ must be $n \times m$.
Thus, order of matrix $B$ is $m \times n$.
Hence, the correct option is (d).
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