Is the operation associative

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Is it known that the multiplication of matrices is a associative operation ?

So,is the relation $(A \cdot B) \cdot C=A \cdot (B \cdot C)$ true??

($A,B,C$ are matrices)

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Yes. This is a well known fact which is proved in any (descent) linear algebra book.

The proof is simple, just calculate both the RHS and the LHS to see both are the same