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Question

If A be any m×n matrix and both AB and BA are defined prove that B should be m×n matrix

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Solution

Since A is m×n and AB defined therefore B should be n×p because the number of columns of A should be equal to number of rows of B.
Again B is row n×p and A is m×n.
And since BA is also defined therefore p should be equal to m by the same argument as above i.e., p = m
B is m×n matrix.

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