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If `A=[(1, 2 ,2 ),(2 ,1 ,2),( 2 ,2, 1)]` , then prove that `A^2-4A-5I=O` .

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If A=[{:(1,2,2),(2,1,2),(2,2,1):}] , then show that A^(2)-4A-5I_(3)=0 . Hemce find A^(-1) .

If A=[1 2 2 2 1 2 2 2 1] , find A^(-1) and prove that A^2-4A-5I=O .

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

If A=[1 2 2 2 1 2 2 2 1] , then show that A^2-4A-5I=O ,w h e r eIa n d0 are the unit matrix and the null matrix of order 3, respectively. Use this result to find A^(-1)dot

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If A=[[4, 2],[-1, 1]] , prove that (A-2I)(A-3I)=O .

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If A = ({:( 1,2,3),( 2,1,2),( 2,2,1) :}) and A^(2) -4A -5l =O where I and O are the unit matrix and the null matrix order 3 respectively if , 15A^(-1) =lambda |{:( -3,2,3),(2,-3,2),(2,2,-3):}| then the find the value of lambda

Show that the matrix A=[[1,2,2],[2,1,2],[2,2,1]] satisfies the equation A^2-4A-5I_3=0 and hence find A^(-1)

RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
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  2. If A=[1 0 2 0 2 1 2 0 3] , then show that A is a root of the polyno...

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  3. If A=[(1, 2 ,2 ),(2 ,1 ,2),( 2 ,2, 1)] , then prove that A^2-4A-5I=O ...

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  4. If A=[(3, 2, 0),( 1, 4 ,0 ),(0 ,0 ,5)] , show that A^2-7A+10 I=O .

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  7. Find the matrix A such that : [4 1 3]A=[-4 8 4-1 2 1-3 6 3] (iv) [2\ \...

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  10. Four uniform spheres, with masses mA=40 kg, mB=35 kg , mC=200 kg , an...

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  12. If A=[(3,-5),(-4, 2)] , then find A^2-5A-14 I . .

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  13. If P(x)=[cosxsinx-sinxcosx] , then show that P(x)P(y)=P(x+y) .

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  14. If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)...

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  15. If A=[(2, 0, 1 ),(2, 1, 3),( 1,-1, 0)] , find A^2-5A+4I and hence fi...

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  16. If [[1,1],[0,1]] , prove that A^n=[[1,n],[0,1]] for all positive int...

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  17. If A=[(a, b),(0, 1)] , prove that A^n=[(a^n,b((a^n-1)/(a-1))),(0 ,1)] ...

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  18. If A=[costhetaisinthetaisinthetacostheta] , then prove by principle...

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  19. If A=[cosalpha+sinalpha,sqrt(2)sinalpha; -sqrt(2)sinalpha,cosalpha-sin...

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  20. If A=[1 1 1 0 1 1 0 0 1] , then use the principle of mathematical in...

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