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Question
Answer the following question:
If A = `[(2, 1),(0, 3)]`, B = `[(1, 2),(3, -2)]`, verify that |AB| = |A||B|
Solution
AB = `[(2, 1),(0, 3)] [(1, 2),(3, -2)]`
= `[(2 + 3, 4 - 2),(0 + 9, 0 - 6)]`
= `[(5, 2),(9, -6)]`
∴ |AB| = `|(5, 2),(9, -6)|`
= –30 – 18
= – 48 ...(1)
|A| = `|(2, 1),(0, 3)|` = 6 – 0 = 6
|B| = `|(1, 2),(3, -2)|` = –2 – 6 = – 8
∴ |A||B| = 6 ( – 8)
= – 48 ...(2)
From (1) and (2),
|AB| = |A||B|
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