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

If `P=[{:(x,0,0),(0,y,0),(0,0,z):}]andQ=[{:(a,0,0),(0,b,0),(0,0,c):}]`, prove that `PQ=[{:(xa,0,0),(0,yb,0),(0,0,zc):}]=QP`.

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`=QP`
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KUMAR PRAKASHAN-MATRICES -Solutions of NCERT Exemplar Problems (Short Answer Type Questions)
  1. Give an example of matrices A,B and C such that AB=AC, where A is nonz...

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

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

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

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

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

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

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

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

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

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

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

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  14. If A=[{:(0,-x),(x,0):}],B=[{:(0,1),(1,0):}]andx^(2)=-1 then show that ...

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  15. Verify that A^(2)=I when A=[{:(0,1,-1),(4,-3,4),(3,-3,4):}].

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  16. Prove by Mathematical Induction that (A)^(n)=(A^(n)) where n inN for a...

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  17. Find inverse , by elementary row operations (if possible), of the foll...

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  18. If [{:(xy,4),(z+6,x+y):}]=[{:(8,w),(0,6):}] , then find values of x,y,...

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  19. If A=[{:(1,5),(7,12):}],B=[{:(9,1),(7,8):}] find a matrix C such that ...

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  20. If A=[{:(3,-5),(-4,2):}], then find A^(2)-5A-14I. Hence , obtain A^(3)...

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