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Question
If A = `[(1, -3),(4, 2)], "B" = [(4, 1),(3, -2)]` show that AB ≠ BA.
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Solution
A = `[(1, -3),(4, 2)], "B" = [(4, 1),(3, -2)]` ...(Given)
AB = `[(1, -3),(4, 2)][(4, 1),(3, -2)]`
= `[(1(4) + (-3)3, 1(1) + (-3)(-2)),(4(4) + 2(3), 4(1) + 2(-2))]`
= `[(4 - 9, 1 + 6),(16 + 6, 4 - 4)]`
= `[(-5, 7),(22, 0)]` ...(1)
BA = `[(4, 1),(3, -2)][(1, -3),(4, 2)]`
= `[(4(1) + 1(4), 4(-3) + 1(2)),(3(1) + (-2)4, 3(-3) + (-2)2)]`
= `[(4 + 4, -12 + 2),(3 - 8, -9 - 4)]`
= `[(8, -10),(-5, -13)]` ...(2)
From (1) and (2), we get,
AB ≠ BA.
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