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Question
Show that AB ≠ BA in each of the following cases:
`A=[[1 3 0],[1 1 0],[4 1 0]]`And B=`[[0 1 0],[1 0 0],[0 5 1]]`
Solution
`A=[[1 3 0],[1 1 0],[4 1 0]]``[[0 1 0],[1 0 0],[0 5 1]]`
`⇒ AB = [[0+3+0 1+0+0 0+0+],[0+1+0 1+0+0 0+0+0],[0+1+0 4+0+0 0+0+0]]`
`⇒AB=[[3 1 0],[1 1 0],[1 4 0]]`...............................(1)
Also,
`BA= [[0 1 0],[1 0 0],[0 5 1]]` `[[1 3 0],[1 1 0],[4 1 0]]`
`⇒BA=[[0+1+0 0+1+1 0+0+0],[1+0+0 3+0+0 0+0+0],[0+5+4 0+5+1 0+0+0]]`
`⇒BA=[[1 1 0],[1 3 0],[9 6 0]]`.......................(2)
∴ AB ≠ BA (From eqs. (1) and (2))
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