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if A=[{:(2,-3),(1,4):}],B=[{:(-1,0),(1,2...

if `A=[{:(2,-3),(1,4):}],B=[{:(-1,0),(1,2):}], C=[{:(3,1),(1,2):}]`, then show that A (BC)=(AB)c.

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The correct Answer is:
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`BC=[{:(-1,0),(1,2):}][{:(3,1),(1,2):}]`
`=[{:(-3+0,-1+0),(3+2,1+4):}]=[{:(-3,-1),(5,5):}]`
`and A(BC) =[{:(2,-3),(1,4):}][{:(-3,-1),(5,5):}]`
`=[{:(-6-15,-2-15),(-3+20,-1+20):}]=[{:(-21,-17),(17,19):}]`
`Now AB=[{:(2,-3),(1,4):}][{:(-1,0),(1,2):}]`
`=[{:(-2-3,0-6),(-1+4,0+8):}]=[{:(-5,-6),(3,8):}]`
`and (AB)C=[{:(-5,-6),(3,8):}][{:(3,1),(1,2):}]`
`=[{:(-15-6,-5-12),(9+8,3+16):}]=[{:(-21,-17),(17,19):}]`
therefore ,A(BC)=(AB)C, Hence proved .
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