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

If `A=[{:(2,3,-1),(1,4,2):}]` and `B=[{:(2,3),(4,5),(2,1):}]` then AB and BA are defined and equal.

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`AB=[(1,-2,3),(-4,2,5)][(2,3),(4,5),(2,1)]`
`=[(2-8+6,3-10+3),(-8+8+10,-12+10+5)]`
`=[(0,-4),(10,3)]`
`BA=[(2,3),(4,5),(2,1)][(1,-2,3),(-4,2,5)]`
`=[(2-12,-4+6,6+15),(4-20,-8+10,12+25),(2-4,-4+2,6+5)]`
`=[(-10,2,21),(-16,2,37),(-2,-2,11)]`
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CENGAGE ENGLISH-MATRICES-ILLUSTRATION
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  2. Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and 11 - n ...

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  3. If A=[{:(2,3,-1),(1,4,2):}] and B=[{:(2,3),(4,5),(2,1):}] then AB and ...

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  4. Find the value of x and y that satisfy the equations [(3,-2),(3,0),(2,...

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  6. If A=[costhetasintheta-sinthetacostheta], then prove that A^n=[cosnthe...

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  7. If A=((p,q),(0,1)), then show that A^(8)=((p^(8),q((p^(8)-1)/(p-1))),(...

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  8. Let A=[(2,1),(0,3)] be a matrix. If A^(10)=[(a,b),(c,d)] then prove th...

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  9. Show that the solutions of the equation [(x,y),(z,t)]^2=0 are[(x,y),(...

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  10. Let a be square matrix. Then prove that A A^(T) and A^(T) A are symmet...

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  11. If A, B are square materices of same order and B is a skewsymmetric ma...

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  12. If a and B are square matrices of same order such that AB+BA=O, then p...

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  13. Let A=[(1,2),(-1,3)] .If A^6=kA-205I then then numerical quantity of...

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  14. Let A, B, C, D be (not necessarily square) real matrices such that A^T...

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  15. If A and B are square matrices of the same order such that A B = B A,...

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  16. If A=[-1 1 0-2] , then prove that A^2+3A+2I=Odot Hence, find Ba n dC m...

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  17. If A=[(3,-4),(1,-1)] then find tr. (A^(2012)).

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  18. If A is a nonsingular matrix satisfying AB-BA=A, then prove that det. ...

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  19. If det, (A-B) ne 0, A^(4)=B^(4), C^(3) A=C^(3)B and B^(3)A=A^(3)B, the...

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  20. Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positiv...

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