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If A B=A and B A=B , then show that A^2=...

If `A B=A` and `B A=B` , then show that `A^2=A` , `B^2=B` .

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. A ,\ B are two matrices such that A B and A+B are both defined; sho...

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  2. If A and B are square matrices of order n , then prove that A and B...

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  3. If A B=A and B A=B , then show that A^2=A , B^2=B .

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  4. Give an example of two matrices A and B such that A!=O ,\ \ B!=O ,\ ...

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  5. Give an example of three matrices A ,\ B ,\ C such that A B=A C but...

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  6. There are 2 families A and B. There are 4 men, 6 women and 2 children ...

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  7. Use matrix multiplication to divide Rs. 30,000 in two parts such that ...

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  8. Three schools A ,\ B and C organised a mela for collecting funds fo...

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  9. Prove that the product of matrices [cos^2thetacosthetasinthetacosthe...

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  10. Let A=[(0,-tan(alpha/2)),(tan(alpha/2),0)] and I be the identity matr...

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  11. Let F(x)=[cosx -sinx 0 sinx cosx 0 ...

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  12. Let A=[2 3-1 2] and f(x)=x^2-4x+7 . Show that f(A)=O . Use this result...

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  13. If A=[0 1 0 0] , prove that (a I+b A)^n=a^n\ I+n a^(n-1)\ b A where I ...

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  14. Let A ,\ B be two matrices such that they commute. Show that for an...

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  15. Let A ,\ B be two matrices such that they commute. Show that for an...

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  16. If A is a square matrix such that A^2=A , show that (I+A)^3=7A+I .

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  17. If A is a square matrix such that A^2=I , then find the simplified...

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

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  19. Compute the indicated products: [a b-b a][a-bb a] (ii) [1-2 2 3][1 ...

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  20. Show that A B!=B A in the following case: A=[5-1 6 7] and B=[2 1 3 ...

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