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Prove that AI=IA=A, for A{:[(2,-1),(4,...

Prove that AI=IA=A, for
`A{:[(2,-1),(4,3)]:},I={:[(1,0),(0,1)]:}`

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`AI{:[(2,-1),(4,3)]:}{:[(1,0),(0,1)]:}={:[(2,-1),(4,3)]:}=A`
`IA={:[(1,0),(0,1)]:}{:[(2,-1),(4,3)]:}={:[(2,-1),(4,3)]:}=A`
`:.AI=IA=A`. Here I is called multiplicative identity matrix.
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PEARSON IIT JEE FOUNDATION-MATRICES-LEVEL 3
  1. Prove that AI=IA=A, for A{:[(2,-1),(4,3)]:},I={:[(1,0),(0,1)]:}

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  2. If A={:[(p,-1),(q,1)]:},B={:[(1,-1),(1,2)]:}and(A+B)^(2)=A^(2)+2AB+B^(...

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  3. If P={:[(2,-1),(-1,3)]:},Q={:[(1,-2),(-3,0)]:}andR={:[(-2,1),(2,-1)]:}...

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  4. If {:((a,3),(4,5)):}{:((3,-2),(b,8)):}={:((30,20),(52,a)):}, then find...

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  5. If P=[2" "2" "1],Q=[1" "2" "3],R={:[(1),(2),(3)]:},andS={:[(3),(2),(1...

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  6. If y={:((4,-2),(3,0)):}andf(y)=y^(2)-y-6, find f(y).

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  7. If the matrix A={:[(5,-3),(5,-3)]:}," then "A^(n+1) = .

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  8. If A(x)={:[(e^(x),e^(x)),(e^(-x),e^(-x))]:} then A(x) A(y)=

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  9. If A={:[(6,-7,1),(3,-2,1)]:}andB={:[(5,1,2),(-4,3,-5)]:} then find X s...

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  10. If {:[(2,4),(p,1)]:}{:[(-1,2),(3,1)]:}={:[(10,q),(-2,r)]:}, then pq= ...

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  11. If A={:[(-13,24),(-7,13)]:}, then A^(8) = .

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  12. If A+B={:[(8,-9),(3,5)]:}andA-B={:[(6,5),(1,7)]:}, the A= .

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  13. If A={:[(7,9),(3,8)]:}andB={:[(13),(18)]:} then find the matrix X such...

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  14. If A={:[(a,b),(2,-1)]:},B={:[(1,1),(4,-1)]and(A+B)^(2)=A^(2)+B^(2), th...

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  15. If A={:[(6,x),(7,-6)]:}andA^(2)=I, then x= .

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  16. If A-B={:[(18,1,-9),(11,12,2)]:}andA+3B={:[(26,1,3),(-13,-16,10)]:}, t...

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  17. If A={:[(1,4),(-2,5)]:}andB={:[(-6,-1),(-8,2)]:}, then AB + BA = .

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  18. If A={:[(2,1),(0,3)]:}andf(x)=x^(2)-4x+3, then find f(A).

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  19. If[5" "6]{:[(1,-3),(-1,x)]:}{:[(3),(4)]:}=[-15], then the value of x ...

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  20. If A={:[(1,-4),(3,2)]:}andB={:[(6,-1),(3,2)]:}, then find the matrix C...

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  21. If A-B^(T)={:[(-2,2,1),(3,6,5)]:}andA^(T)+B={:[(-4,5),(8,-2),(9,1)]:},...

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