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If `G` is the set of all matrices of the form `[xxxx]` , where `x in R-{0}` , then the identity element with respect to the multiplication of matrices as binary operation, is `[1 1 1 1]` (b) `[-1//2-1//2-1//2-1//2]` (c) `[1//2 1//2 1//2 1//2]` (d) `[-1-1-1-1]`

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`AE=A=>[[x, x], [x, x]][[e, e], [e, e]]=[[x, x][x, x]]`
`[[2ex, 2ex], [2ex, 2ex]]=[[x, x], [x, x]]`
`2ex=x=>x=1/2`
`e=[[1/2, 1/2], [1/2, 1/2]]`
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. If a binary operation * is defined on the set Z of integers as a ast...

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  2. Q^+ denote the set of all positive rational numbers. If the binary ope...

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  3. If G is the set of all matrices of the form [xxxx] , where x in R-...

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  4. Q^+ is the set of all positive rational numbers with the binary ope...

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  5. If the binary operation o. is defined on the set Q^+ of all positive r...

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  6. Let * be a binary operation defined on set Q-{1} by the rule a*b=a+b...

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  7. Which of the following is true? * defined by a*b=(a+b)/2 is a binar...

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  8. The binary operation * defined on N by a*b=a+b+a b for all a ,\ b i...

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  9. If a binary operation * is defined by a*b=a^2+b^2+a b+1 , then (2*3...

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  10. Let * be a binary operation on R defined by a*b=a b+1 . Then, * is ...

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  11. Subtraction of integers is

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  12. The law a+b=b+a is called

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  13. An operation * is defined on the set Z of non-zero integers by a*b=a/...

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  14. On Z an operation * is defined by a * b=a^2+b^2 for all a ,\ b in Z...

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  15. A binary operation ast on Z defined by a ast b=3a+b for all a ,\ b i...

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  16. Letastbe a binary operation on N defined by a ast b=a+b+10 for all a...

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  17. Consider the binary operation ast defined on Q-{1} by the rule a ast...

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  18. For the binary operation ast defined on R-{-1} by the rule a ast b=a...

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  19. For the multiplication of matrices as a binary operation on the set ...

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  20. On the set Q^+ of all positive rational numbers a binary operation *...

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