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If A={:[(1,2,0),(-1,0,1),(1,2,1)]:},B={:...

If `A={:[(1,2,0),(-1,0,1),(1,2,1)]:},B={:[(1,2),(2,1),(-1,1)]:}andC={:[(1,0,0,1),(1,2,1,2)]:}` Find A(BC), (AB)C and prove that A(BC)=(AB)C.

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`A={:[(1,2,0),(-1,0,1),(1,2,1)]:},B={:[(1,2),(2,1),(-1,1)]:},C={:[(1,0,0,1),(1,2,1,2)]:}`
`BC={:[(1,2),(2,1),(-1,1)]:}{:[(1,0,0,1),(1,2,1,2)]:}={:[(3,4,2,5),(3,2,1,4),(0,2,1,1)]:}`
Now, A(BC)= `{:[(1,2,0),(-1,0,1),(1,2,1)]:}{:[(3,4,2,5),(3,2,1,4),(0,2,1,1)]:}={:[(9,8,4,13),(-3,-2,-1,-4),(9,10,5,14)]:}`
Now, AB `={:[(1,2,0),(-1,0,1),(1,2,1)]:}{:[(1,2),(2,1),(-1,1)]:}={:[(5,4),(-2,-1),(4,5)]:}`
Now, (AB)C `={:[(5,4),(-2,-1),(4,5)]:}{:[(1,0,0,1),(1,2,1,2)]:}`
`={:[(9,8,4,13),(-3,-2,-1,-4),(,10,5,14)]:}`
Clearly, A(BC)=(AB)C
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