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If A is any mxxn such that A B and B A a...

If `A` is any `mxxn` such that `A B` and `B A` are both defined show that `B` is an `nxxm` matrix.

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RD SHARMA ENGLISH-ALGEBRA OF MATRICES-All Questions
  1. If A=[(1 1 1),( 1 1 1),( 1 1 1)] , then prove that A^n=|(3^(n-1)3^(n-1...

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  2. Under what conditions is the matrix equation A^2-B^2=(A-B)(A+B) is ...

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  3. If A is any mxxn such that A B and B A are both defined show that B...

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  4. A ,\ B are two matrices such that A B and A+B are both defined; sho...

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

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

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

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

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

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

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

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

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

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

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  15. 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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  16. 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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  17. Let A ,\ B be two matrices such that they commute. Show that for an...

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

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

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

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