Replying to Math problem (binary operation)

can anybody help me prove that this binary operation is associative (a*(b*c) = (a*b)*c)? the operation is this. suppose you have a class full of desks in a rectangular formation. the kids names are a b c d e f... and we have to prove that the operation is associative. a*(b*c) means that you take student a's row and student (b*c)'s colum and find the person that the row and colum both have in common. any help? ive done tons of examples and they all work, but i dont know how to prove it.

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