If A is a matrix of order m × n and B is a matrix such that
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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