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प्रश्न
Show that AB ≠ BA in each of the following cases
`A=[[-1 1 0],[0 -1 1],[2 3 4]]` and =B `[[1 2 3], [0 1 0],[1 1 0]]`
उत्तर
`A=[[-1 1 0],[0 -1 1],[2 3 4]]` `[[1 2 3], [0 1 0],[1 1 0]]`
`⇒AB=[[-1+0+0 -2+1+0 -3+0+0],[0+0+1 0-1+1 0+0+0],[2+0+4 4+3+4 6+0+0]]`
`⇒AB=[[-1 -1 -3],[1 0 0],[6 11 6]]`
Also,
`BA= [[1 2 3],[0 1 0],[1 1 0]]``[[-1 1 0],[0 -1 1],[2 3 4]]`...................(1)
`⇒BA = [[-1+0+6 1-2+9 0+2+12],[0+0+0 0-1+0 0+1+0],[-1+0+0 1-1+0 0+1+0]]`
`⇒BA=[[5 8 14],[0 -1 1],[-1 0 1]]`.......................(2)
∴ AB ≠ BA From eqs. (1) and (2)
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