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If `A = [(1, 3),(2, 4)], B = [(1, 2),(4, 3)] and C = [(4, 3),(1, 2)]` Find 1) (Ab)C 2) A(Bc) is A(Bc) = (Ab)C? - ICSE Class 10 - Mathematics

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Question

If `A = [(1, 3),(2, 4)], B = [(1, 2),(4, 3)] and C = [(4, 3),(1, 2)]` find 

1) (AB)C

2) A(BC)

Is A(BC) = (AB)C?

Solution

1)`AB = [(1, 3),(2, 4)][(1, 2),(4, 3)] = [(1 + 12, 2+9),(2 + 16, 4 + 12)] = [(13, 11), (1, 2)]`

`(AB)C = [(13, 11),(18, 16)][(4, 3),(1, 2)] = [(52 + 11, 39 + 22),(72 + 16, 54 + 32)] = [(63, 61),(88, 86)]`

2) `BC = [(1, 2),(4, 3)] = [(4 + 2, 3 + 4),(16 + 3, 12 + 6)] = [(6, 7),(19, 18)]`

`A(BC) = [(1, 3),(2, 4)][(6, 7),(19, 18)] = [(6 + 57,7 + 54),(12 + 76, 14 + 72)] = [(63, 61),(88, 86)]`

hence A(BC) = (AB)C

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Solution If `A = [(1, 3),(2, 4)], B = [(1, 2),(4, 3)] and C = [(4, 3),(1, 2)]` Find 1) (Ab)C 2) A(Bc) is A(Bc) = (Ab)C? Concept: Multiplication of Matrix.
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