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Show by an example that for AneO,BneO,AB...

Show by an example that for `AneO,BneO,AB=O`.

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The correct Answer is:
`=O`
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KUMAR PRAKASHAN-MATRICES -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. If A=[{:(3,-4),(1,1),(2,0):}]andB=[{:(2,1,2),(1,2,4):}],then verify (B...

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  2. If possible , find BA and AB , where A=[{:(2,1,2),(1,2,4):}],B=[{:...

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  3. Show by an example that for AneO,BneO,AB=O.

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  4. Given A=[{:(2,4,0),(3,9,6):}]andB=[{:(1,4),(2,8),(1,3):}]. Is (AB)'=B'...

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  5. Solve for x and y : x[{:(2),(1):}]+y[{:(3),(5):}]+[{:(-8),(-11):}]=...

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  6. If X and Y are 2xx2 matrices , then solve the following matrix equati...

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  7. If A=[3" " 5],B=[7" " 3] , then find a non - zero matrix C such tha...

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  8. Give an example of matrices A,B and C such that AB=AC, where A is nonz...

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  9. If A=[{:(1,2),(-2,1):}],B=[{:(2,3),(3,-4):}]andC=[{:(1,0),(-1,0):}] ve...

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  10. If P=[{:(x,0,0),(0,y,0),(0,0,z):}]andQ=[{:(a,0,0),(0,b,0),(0,0,c):}], ...

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  11. If [[2" "1" "3][{:(-1,0,-1),(-1,1,0),(0,0,1):}]*[{:(1),(0),(-1):}]=A f...

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  12. If A=[2" "1],B=[{:(5,3,4),(8,7,6):}]andC=[{:(-1,2,1),(1,0,2):}], veri...

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  13. If A=[{:(1,0,-1),(2,1,3),(0,1,1):}] , then verify that A^(2)+A=A(A+I)...

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  14. If A=[{:(0,-1,2),(4,3,-4):}]andB=[{:(4,0),(1,3),(2,6):}] then verify ...

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  15. If A=[{:(1,2),(4,1),(5,6):}],B=[{:(1,2),(6,4),(7,3):}], then verify th...

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  16. Show that A'A and A A ' are both symmetric matrices for any matrix A .

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  17. Let A and B be square matrices of the order 3xx3 . Is (AB)^(2)=A^(2)B^...

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  18. Show that if A and B are square matrics such that AB=BA , then (A+B)^(...

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  19. Let A=[{:(1,2),(-1,3):}],B=[{:(4,0),(1,5):}],C=[{:(2,0),(1,-2):}]and a...

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  20. If A=[{:(cosq,sinq),(-sinq,cosq):}] , then show that A^(2)=[{:(cos(2q...

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