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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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False,
Since AB is defined
`therefore AB=[{:(2,3,-1),(1,4,2):}][{:(2,3),(4,5),(2,1):}]=[{:(14,20),(22,25):}]`
Also, BA is defined
`therefore BA=[{:(2,3),(4,5),(2,1):}][{:(2,3,-1),(1,4,2):}]`
`=[{:(7,18,4),(13,32, 6),(5,10,0):}]`
`ABneBA`
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NCERT EXEMPLAR ENGLISH-MATRICES-Solved example
  1. A matrix denotes a number

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  2. Matrices of any order can be added.

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  3. Two matrices are equal. If they have same number of rows and same numb...

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  4. Matrices of different order cannot be subtracted.

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  5. Matrix addition is associative as well as commutative.

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  6. Matrix m ultiplication is commutative.

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  7. A square m atrix where every element is unity is called an identity ma...

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  8. If A and B are two square matrices of the same order, then A+B=B+A.

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  9. If A and B are two m atrices of the same order, then A-B=B-A.

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  10. If A dn B be 3xx3 matrices the AB=0 implies (A) A=0 or B=0 (B) A=0 and...

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  11. Transpose of a column matrix is a column matrix.

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

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  13. If each of the three matrices of the same order are symmetric, then th...

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  14. If A and B are any two matrices of the same order, then (AB)=A'B'

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  15. If (AB)=BA, where A and B are not square matrices, then number of rows...

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  16. Let A; B; C be square matrices of the same order n. If A is a non sing...

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  17. A A' is always a symmetric matrix for any matrix A.

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

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  19. If A is skew-symmetric matrix then A^(2) is a symmetric matrix.

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  20. If A; B are invertible matrices of the same order; then show that (AB)...

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