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Question
Show that AB ≠ BA in each of the following cases:
`A= [[5 -1],[6 7]]`And B =`[[2 1],[3 4]]`
Solution
`A= [[5 -1],[6 7]]` `[[2 1],[3 4]]`
`⇒ AB= [[10-3 5-4],[12+21 6+28]]`
`⇒AB=[[7 1],[33 34]]`..............................(1)
Also,
`BA = [[2 1],[3 4]][[5 -1],[6 7]]`
`⇒BA=[[10+6 -2+7],[15+24 -3+28]]`
`⇒BA=[[16 5],[39 25]]`................(2)
`∴AB ≠ BA ` (From eqs. (1) and (2))
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