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Matrix addition is associative as well a...

Matrix addition is associative as well as commutative .

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Matrix subtraction is associative

Consider the binary operations * : R xx R to R and o: R xx R to R defined as a * b = |a-b| and a o b = a for all a,b in R . Show that '*' is commutative but not associative, 'o' is associative but not commutative.

Addition is commutative for

Consider the operations '*' and o+ on the set R of all real numbers defined as a* b = |a-b| and a o+ b = a for all a, b in R. Prove that o+ is associative but n ot commutative.

Consider the binary operations * : RxxRrarrR and o : RxxRrarrR defined as a*b = |a – b| and aob = a, forall a, b in R Show that ∗ is commutative but not associative, o is associative but not commutative. Further, show that ∀ a, b, c in R , a * (b o c) = (a * b) o (a * c) . [If it is so, we say that the operation ∗ distributes over the operation o]. Does o distribute over ∗? Justify your answer.

Determine the following binary operations on the set R are associative or commutative: a*b = (a+b)/2, forall a,b in R

True or False statements : Matrix addition is not associative.

Show that the binary operation on the set 'N' given by a * b =1 AA a,b in N is commutative as well as associative.

Matrix multiplication is commutative .

Give an examples of a matrix which is a row as well as a column matrix.

ACCURATE PUBLICATION-MATRICES-QUESTIONS CARRYING 1 MARK (Type-III : (True or false questions))
  1. Two matrices are equal if they have same number of rows and same numbe...

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  2. Matrices of different order can not be subtracted .

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  3. Matrix addition is associative as well as commutative .

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  4. Matrix multiplication is commutative .

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  5. A square matrix where every element is unity is called an identity mat...

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

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  7. If A and B are two matrices of the same order, then A-B=B-A .

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  8. If matrix AB=O, then A=O or B=O or both A and B are null matrices .

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  9. Transpose of a column matrix is a column matrix .

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  10. If A and B are two square matrices of the same order, then AB=BA .

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  11. If each of the three matrices of the same order are symmetric then the...

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  12. If A and B are two square matrices of the same order, then AB=BA .

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  13. If (AB)=B'A' , where A and B are not square matrices, then number of r...

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  14. If A, B and C are square matrices of same order, then AB=AC always imp...

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

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

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  17. If A is skew symmetric matrix, then A^(2) is a symmetric matrix .

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  18. (AB)^(-1)=A^(-1)B^(-1), where A and B are invertible matrices satisfyi...

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  19. The number of all possible matrices of order 3xx3 with each entry 0 or...

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  20. If matrix A is of order 4 xx 3, then each row of matrix A contains ele...

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