Show that if A is an [m x n] matrix and A(BA) is defined, then B is an [n x m] matrix.

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- Jun 16th 2009, 04:29 PMchriscdetermining matrix size
Show that if A is an [m x n] matrix and A(BA) is defined, then B is an [n x m] matrix.

- Jun 16th 2009, 05:07 PMpickslides
If A has order $\displaystyle m\times n$ look at BA first of all

For be BA to be defined B must have order $\displaystyle k\times m$ in turn BA must have order $\displaystyle k\times n$

Now for A(BA) to be defined $\displaystyle k=n$ therefore B has order $\displaystyle n\times m$ - Jun 23rd 2009, 02:27 PMchrisc
thank you, easy to understand when its right in front of me (Hi)