Hi I;m just learning suffix notation and the summation convention.

Just to check my understanding can someone just check to see if I've done this right,

I've done it like soDefine a new sort of multiplication by

$\displaystyle (\bf{A} \bullet \bf{B})_{ij}=(\bf{A})_{ik}(\bf{B})_{jk}$

Using suffix notation show that bullet multiplication isn't associative

$\displaystyle ((\bf{A} \bullet \bf{B}) \bullet \bf{C})_{ij} = (\bf{A} \bullet \bf{B})_{ik}(\bf{C})_{jk}=(\bf{A})_{im}(\bf{B})_{k m}(\bf{C})_{jk}$

$\displaystyle (\bf{A} \bullet (\bf{B} \bullet \bf{C}))_{ij}=(\bf{A})_{ik}(\bf{B} \bullet \bf{C})_{jk}=(\bf{A})_{jk}(\bf{B})_{jm}(\bf{C})_{k m}$

As the components aren't equal bullet multiplication isn't associative