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प्रश्न
If A =
\[\begin{bmatrix}2 & - 3 & - 5 \\ - 1 & 4 & 5 \\ 1 & - 3 & - 4\end{bmatrix}\]and B =
\[\begin{bmatrix}- 1 & 3 & 5 \\ 1 & - 3 & - 5 \\ - 1 & 3 & 5\end{bmatrix}\] , show that AB = BA = O3×3.
उत्तर
Here ,
AB= `[[2 -3 -5],[-1 4 5],[1 -3 -4]]``[[-1 3 5],[1 -3 -5],[-1 3 5]]`
`⇒AB =[[-2-3+5 6+9- 15 10+15-25],[1+4-5 -3-12+15 -5-20=25],[-1-3+4 3+9-12 5+15-20]]`
`⇒AB=[[0 0 0],[0 0 0],[0 0 0]]`
`⇒AB = O3xx3` .................(1)
`⇒BA=[[-1 3 5],[1 -3 -5],[-1 3 5]]``[[2 -3 -5],[-1 4 5],[1 -3 -4]]`
`⇒BA=[[-2-3+5 3+12-15 5+15-20],[2+3-5 -3-12+15 -5-15+20],[-2-3+5 3+12-15 5+15-20]]`
`⇒BA=[[0 0 0 ],[0 0 0],[0 0 0]]`
`⇒BA=0_3×3` ...(2)
`⇒AB=BA=0_3×3 ` [From eqs. (1) and (2)]
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