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i) Prove if $\langle A,B\rangle$ is a binary operation.

ii) Is it associative? is it commutative?

ie $ A= (a_1 ,a_2 ) \space B= (b_1 , b_2) $ and A dot B $= a_1 b_1 + a_2 b_2 $

im kind of lost here $\langle A,B\rangle$ is a vector of two variables to only 1 number it doesn't look like a binary operation at all the concept of associativity doesn't seem to be defined but it is defiantly commutative!

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    Binary or bilinear? – 2017-01-11
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    uh whichever one you find in an introduction to binary operations/ groups class? if i said i dont know what the diffrence was would that answer the question? – 2017-01-11
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    Yeah, everything you said is true. Dot product not a binary operation, associativity doesn't even make sense. – 2017-01-11
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    In general, for an inner-product space $(V,\langle\cdot,\cdot\rangle$), over a field $F$, the inner product is a function $V \times V \to F$, whereas a binary operation on $V$ would be a function $V \times V \to V$. If $V$ is a one-dimensional inner product space (that is, $V = F$ for some field $F$), then the inner product *would* be a binary operation-for the vector space $\Bbb R$ (over itself), the usual dot product becomes ordinary real multiplication. – 2017-01-12

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