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If A=[{:(,),(,):}]andB=[{:(,),(,):}] , t...

If `A=[{:(,),(,):}]andB=[{:(,),(,):}]` , then find the matrices `A^(2),B^(2),A+B,A-BandA^(2)-B^(2)`.
Is `A^(2)-B^(2)=(A+B) (A-B)`?

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Verified by Experts

The correct Answer is:
`A-B=[{:(0,-1),(0,0):}],A^(2)-B^(2)=[{:(0,-5),(0,0):}]` ; not equal
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ARIHANT PUBLICATION-MATRICES -CHAPTER PRACTICE (Very Short Answer Type Questions)
  1. If possible then find the value of BA and AB , where A=[{:(2,1,2),(1,2...

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

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  3. If A=[{:(,),(,):}]andB=[{:(,),(,):}] , then find the matrices A^(2),B^...

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  4. If A=[{:(0,1),(1,1):}]andB=[{:(0,-1),(1,0):}], then show that (A+B)(A-...

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

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  6. If A=[{:(0,6,7),(-6,0,8),(7,-8,0):}],B=[{:(0,1,1),(1,0,2),(1,2,0):}]an...

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  7. How many different matrix products can you form with these three matri...

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  8. Solve the matrix [{:(x,-5,-1):}][{:(1,0,2),(0,2,1),(2,0,3):}][{:(x),(4...

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  9. If A(alpha)=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}], then prove...

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  10. If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] , then find the va...

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

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  12. Find the matrix A satisfying the equation [{:(2,1),(3,2):}].A.[{:(-3...

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  13. If A=[{:(1,0,2),(0,2,1),(2,0,3):}], then prove that A is a root of th...

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  14. Let A=[{:(2,3),(-1,2):}]andf(x)=x^(2)-4x+7 . Show that f(A)=O. Use thi...

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  15. If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] , then find A^(2)-5A+6I.

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  16. If A=[{:(2,3),(1,2):}], then prove that A^(3)-4A^(2)+A=O.

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  17. If A=[{:(1,0),(-1,7):}], thenfind k such that A^(2)-8A+kI=O.

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  18. If A=[{:(3,-2),(4,-2):}], then find k such that A^(2)=kA-2I .

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  19. For the matrix A=[{:(3,1),(7,5):}] , find a and b such that A^(2)+aI...

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  20. Given that, A=[{:(4,0),(2k,5k):}] and B=[{:(k,0),(3,-1):}] such that A...

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