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Question
If A = `[(2, 1),(0, 0)]`, B = `[(2, 3),(4, 1)]` and C = `[(1, 4),(0, 2)]`; then show that A(B + C) = AB + AC.
Solution
B + C = `[(2, 3),(4, 1)] + [(1, 4),(0, 2)] = [(3, 7),(4, 3)]`
A(B + C) = `[(2, 1),(0, 0)][(3, 7),(4, 3)]`
= `[(6 + 4, 14 + 3),(0 ,0)]`
= `[(10, 17),(0 ,0)]`
AB = `[(2, 1),(0, 0)][(2, 3),(4, 1)]`
= `[(4 + 4, 6 + 1),(0, 0)]`
= `[(8, 7),(0, 0)]`
AC = `[(2, 1),(0, 0)][(1, 4),(0, 2)]`
= `[(2 + 0, 8 + 2),(0, 0)]`
= `[(2, 10),(0, 0)]`
AB + AC = `[(8, 7),(0, 0)] + [(2, 10),(0, 0)]`
= `[(10, 17),(0, 0)]`
Hence, A(B + C) = AB + AC
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