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If A=[(2,-3,-5),(-1, 4, 5),( 1,-3,-4)] a...

If `A=[(2,-3,-5),(-1, 4, 5),( 1,-3,-4)]` and `B=[(-1, 3, 5),( 1,-3,-5),(-1 ,3, 5)]` , show that `A B=B A=0_3xx3` .

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Given,
`A=[(2,-3,-5),(-1, 4, 5),( 1,-3,-4)]`
`B=[(-1, 3, 5),( 1,-3,-5),(-1 ,3, 5)]`
`AB=[(2,-3,-5),(-1, 4, 5),( 1,-3,-4)]xx[(-1, 3, 5),( 1,-3,-5),(-1 ,3, 5)]`
`=[(-2-3+5, 6+9-15, 5+15-20),( 1+4-5,-3-12+15,-5-15+20),(-1-3+4 ,3+9-12, 5+15-20)]`
`=[(0, 0, 0),( 0,0,0),(0,0, 0)]`
`BA=[(-1, 3, 5),( 1,-3,-5),(-1 ,3, 5)]xx[(2,-3,-5),(-1, 4, 5),( 1,-3,-4)]`
`=[(-2-3+5, 3+12-15, 5+15-20),( 2+3-5,-3-12+15,-5-15+20),(-2-3+5 ,3+9-12, 5+15-20)]`
`=[(0, 0, 0),( 0,0,0),(0,0, 0)]`
hence `A B=B A=0_(3xx3)`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
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  2. If A=[(cos2theta,sin2theta),(-sin2theta,cos2theta)] , find A^2 .

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  3. If A=[(2,-3,-5),(-1, 4, 5),( 1,-3,-4)] and B=[(-1, 3, 5),( 1,-3,-5),(-...

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  12. If omega is a complex cube root of unity, show that ([(1,omega,omega...

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  13. If A=[(2,-3,-5),(-1 ,4 ,5),( 1,-3,-4)] , show that A^2=A .

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  14. If A=[(4,-1,-4 ),(3, 0,-4),( 3,-1,-3)] , show that A^2=I3

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  15. If [1\ \ 1\ \ x][1 0 2 0 2 1 2 1 0][1 1 1]=0 , find xdot

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  16. If [(2,3),(5,7)][(1,-3),(-2,4)]=[(-4,6),(-9,x)] , find xdot

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  17. If [(x,4,1)][(2,1,2),(1,0,2),(0,2,-4)][(x),(4),(-1)]=0 , find xdot

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  18. If [(1, -1,x)][(0 ,1,-1),( 2 ,1 ,3),( 1 ,1 ,1)][(0),( 1),( 1)]=0 , fin...

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  19. If A=[(3,-2),( 4,-2)] and I=[(1 ,0),( 0 ,1)] , then prove that A^2-A+2...

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  20. If A=[(3 ,1),(-1, 2)] and I=[(1, 0), (0 ,1)] , then find lambda so tha...

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