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Well I think it's all in the title..anyway..I would like to know through which passages did Binet get to his matrix multiplication algorithm and where (book, paper..) did he first tell about it to the world

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You might want to peruse some findings of of Oliver Knill (Harvard):

When was Matrix Multiplication Invented?

You'll find a number of potential resources to dig further. It is mentioned that Binet discussed such an algorithm in a lecture dated November 30, 1812.

From Wikipedia: Binet is "recognized as the first to describe the rule for multiplying matrices in 1812."

If it's of any solace, you might like the quote you can find on the linked webpage:

To give the history of linear algebra is a task that is as important as it is difficult.
--Nicolas Bourbaki, 1984

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ouch!..what a pity! Unfortnately I had already got to that page..helpful (the page I mean) but yet not satisfactory..I wonder whether there's any trace of the text of that lecture around..I'm going to look up right now –  Matteo Nov 29 '12 at 17:20

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