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

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  2. In which of the following type of matrix inverse does not exist always...

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  3. If both A-1/2Ia n dA+1/2 are orthogonal matices, then (a)A is ortho...

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  4. If nth-order square matrix A is a orthogonal, then |adj(adjA)| is (...

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  5. If P is an orthogonal matrix and Q=P A P^T an dx=P^T Q^1000 P then x^...

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  6. If A is a nilpotent matrix of index 2, then for any positive integer n...

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  7. If Aa n dB are two matrices such that A B=Ba n dB A=A ,t h e n (A^5-B...

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  8. If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. ...

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  9. If A is an orthogonal matrix then A^(-1) equals A^T b. A c. A^2 d. non...

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  10. If A^2=1, then the value of det(A-I) is (where A has order 3) 1 b. -1 ...

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  11. Let A be an nth-order square matrix and B be its adjoint, then |A B+K ...

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  12. A=[(a,1,0),(1,b,d),(1,b,c)],B=[(a,1,1),(0,d,c),(f,g,h)],U=[(f),(g),(h)...

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  13. If M is a 3 xx 3 matrix, where det M=1 and MM^T=1, where I is an ident...

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  14. If A is a diagonal matrix of order 3xx3 is commutative with every squa...

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  15. Let S be the set which contains all possible vaues fo I ,m ,n ,p ,q ,r...

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  16. 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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  17. If A is a square matrix of order 3 such that |A|=2,t h e n|(a d jA^(-1...

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  18. Let A=[[3x^2], [1], [6x]],B=[a,b,c]and C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2...

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  19. If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h...

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  20. Let A=([a(i j)])(3xx3) be a matrix such that AA^T=4Ia n da(i j)+2c(i j...

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  21. Let A be the set of all 3xx3 skew-symmetri matrices whose entries are ...

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