If A=[(1, 0,-2 ),(3,-1, 0),(-2, 1, 1)] ,...

If `A=[(1, 0,-2 ),(3,-1, 0),(-2, 1, 1)]` , `B=[(0 ,5,-4),(-2, 1 ,3),(-1, 0, 2)]` and `C=[(1, 5, 2),(-1 ,1, 0),( 0,-1, 1)]` , verify that `A(B-C)=A B-A C`

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Given that,
`A=[(1, 0,-2 ),(3,-1, 0),(-2, 1, 1)]`
`B=[(0 ,5,-4),(-2, 1 ,3),(-1, 0, 2)]`
and `C=[(1, 5, 2),(-1 ,1, 0),( 0,-1, 1)]`
`text(LHS)=A(B-C)`
`=[(1, 0,-2 ),(3,-1, 0),(-2, 1, 1)]([(0 ,5,-4),(-2, 1 ,3),(-1, 0, 2)]-[(1, 5, 2),(-1 ,1, 0),( 0,-1, 1)])`
`=[(1, 0,-2 ),(3,-1, 0),(-2, 1, 1)][(-1,0,-6),(-1,0,3),(-1,1,1)]`
`=[(1,-2,-8),(-2,0,-21),(0,1,16)]`
`text(RHS)=A B-A C`
`=[(1, 0,-2 ),(3,-1, 0),(-2, 1, 1)][(0 ,5,-4),(-2, 1 ,3),(-1, 0, 2)]-[(1, 0,-2 ),(3,-1, 0),(-2, 1, 1)][(1, 5, 2),(-1 ,1, 0),( 0,-1, 1)]`
`=[(2,5,-8),(2,14,-15),(-3,-9,-9)]-[(1,7,0),(4,14,6),(-3,-10,-3)]`
`=[(1,-2,-8),(-2,0,-21),(0,1,16)]`
hence `A(B-C)=A B-A C`

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