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Question
If A is a 3 × 4 matrix and B is a matrix such that both ATB and BAT are defined, what is the order of the matrix B?
Solution
A is a matrix of order 3 × 4
So AT will be a matrix of order 4 × 3
ATB will be defined when B is a matrix of order 3 × n
BAT will be defined when B is of order m × 4
From (1) and (2) we see that B should be a matrix of order 3 × 4
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