Let A{:[(5,10),(10,20)]:},{:[(10,5),(15,...

Let `A{:[(5,10),(10,20)]:},{:[(10,5),(15,10)]:}and={:[(-10,35),(25,-5)]:}`. Prove that AB = AC but `B!=C`

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`AB={:[(5,10),(10,20)]:}{:[(10,5),(15,10)]:}`
`={:[((5)10+10(15),(5)5+(10)10),((10)10+(20)15,(10)5(20)10)]:}`
`={:[(50+150,25+100),(100+300,50+200)]:}={:[(200,125),(400,250)]:}`
`AC={:[(5,10),(10,20)]:}{:[(-10,35),(25,-5)]:}`
`={:[(5(-10)+10(25),5(35)+10(-5)),(10(-10)+20(25),10(35)+20(-5))]:}`
`={:[(-50+250,175-50),(-100+500,350-100)]:}`
`={:[(200,125),(400,250)]:}`.
Here AB=AC but `B!=C`.
Hence Proved.

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