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

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Given,
`A=[(2,-3,-5),(-1, 4 ,5),( 1,-3,-4)]`
`B=[(2,-2,-4),(-1 ,3, 4 ),(1,-2,-3)]`
`AB=[(2,-3,-5),(-1, 4 ,5),( 1,-3,-4)]xx[(2,-2,-4),(-1 ,3, 4 ),(1,-2,-3)]`
`=[(4+3-5,-4-9+10,-8-12+15),(-2-4+5 ,2+12-10, -4-12+12 ),(-2+3-4,-2-9+8,-4-12+12)]`
`= [(2,-3,-5),(-1, 4 ,5),( 1,-3,-4)]=A`
`BA=[(2,-2,-4),(-1 ,3, 4 ),(1,-2,-3)]xx[(2,-3,-5),(-1, 4 ,5),( 1,-3,-4)]`
`=[(4+2-4,-6-8+12,-10-10+16),(-2-3+4,3+12-12, 5+15-16 ),(2+2-3,-3+9-8,-5-10+12)]`
`=[(2,-2,-4),(-1 ,3, 4 ),(1,-2,-3)]=B`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. If A=[(2,-3,-5),(-1, 4, 5),( 1,-3,-4)] and B=[(-1, 3, 5),( 1,-3,-5),(-...

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  2. If A=[(0,c,-b),(-c,0,a),( b,-a,0)] and B=[(a^2,a b, a c),( a b,b^2,b c...

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

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  4. Let A=[(-1, 1,-1 ),(3,-3, 3 ),(5, 5, 5)] and B=[(0 ,4 ,3),( 1,-3,-3),(...

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  5. For the following matrices verify the associativity of matrix multip...

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  6. For the following matrices verify the distributivity of matrix multi...

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  7. If A=[(1, 0,-2 ),(3,-1, 0),(-2, 1, 1)] , B=[(0 ,5,-4),(-2, 1 ,3),(-1, ...

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  8. Compute the elements a(43) and a(22) of the matrix: A=[(0 ,1, 0),( 2, ...

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  9. If A=[(0 ,1 ,0),( 0, 0, 1),(p, q ,r)] and I is the identity matrix o...

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

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

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

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

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

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

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

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

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

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  19. If A=[[3 ,1],[-1, 2]] , show that A^2-5A+7I2=O .

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  20. If A=[(2, 3),(-1 ,0)] , show that A^2-2A+3I2=O .

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