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# If A is matrix of order $m\times n$ and B is a matrix such that AB' and B'A are both defined,then order of matrix B is

\begin{array}{1 1}(A)\quad m\times m & (B)\quad n\times n\\(C)\quad n\times m & (D)\quad m\times n\end{array}
Can you answer this question?

Order of matrix A$\rightarrow m\times n.$
A${B' }$&${B'}$ A$\rightarrow$ defined.
Order of matrix B=$m\times n$.
Answer is (D).Let B$\rightarrow p\times q$
Since A$B'$&$B'$A is defined P=m,n=q.
Hence order of matrix $B=m\times n.$
answered Jul 13, 2013