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प्रश्न
Let A = `[(1, 2),(-1, 3)]`, B = `[(4, 0),(1, 5)]`, C = `[(2, 0),(1, -2)]` and a = 4, b = –2. Show that: A(BC) = (AB)C
उत्तर
We have,
A = `[(1, 2),(-1, 3)]`
B = `[(4, 0),(1, 5)]`
C = `[(2, 0),(1, -2)]`
And a = 4, b = –2
(BC) = `[(4, 0),(1, 5)] [(2, 0),(1, -2)]`
= `[(8, 0),(7, -10)]`
And A(BC) = `[(1, 2),(-1, 3)] [(8, 0),(7, -10)]`
= `[(8 + 14,0 - 20),(-8 ++21, 0 - 30)]`
= `[(22, -20),(13,-30)]`
Also, AB = `[(1, 2),(-1, 3)] * [(4, 0),(1, 5)]`
= `[(4 + 2, 0 + 10),(-4 + 3, 0 +15)]`
= `[(6, 10),(-1, 15)]`
∴ (AB)C = `[(6, 10),(-1, 15)] [(2, 0),(1, -2)]`
= `[(22, -20),(13, -30)]`
= A(BC)
Hence proved.
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