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Check commutativity and associativity `@` on `M_(2)(RR)` defined by `A@B=(1)/(2)(AB-BA)` for all `A,BinM_(2)(RR)` where `M_(2)(RR)` is a `2xx2` real matrix.

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The correct Answer is:
Neither commutative nor associative
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CHHAYA PUBLICATION-BINARY OPERATION-EXERCISE 3 (Short Answer Type Questions)
  1. Discuss the commutativity and associativity ** on RR defined by a**b=|...

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  2. ** on ZZxxZZ defined by (a,b)**(c,d)=(a-c,b-d) for all (a,b),(c,d)inZZ...

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  3. Check commutativity and associativity @ on M(2)(RR) defined by A@B=(1)...

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  4. An operation ** on ZZ, the set of integers, is defined as, a**b=a-b+ab...

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  5. (I) Let ** be a binary operation defined by a**b=2a+b-3. Find 3**4. ...

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  6. A binary operaiton @ is defined on the set RR-{-1} as x@y=x+y+xy for a...

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  7. If ** be the binary operation on the set ZZ of all integers, defined b...

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  8. A binary operation @ is defined on ZZ, the set of integers, by a@b=|a-...

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  9. Let ** a binary operation on NN given by a**b=H.C.F (a,b) for all a,bi...

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  10. If +(6) (addition modulo 6) is a binary operation on A={0,1,2,3,4,5},...

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  11. A binary operation ** is defined on the set RR(0) for all non- zero re...

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  12. A binary operation ** is defined on the set ZZ of all integers by a@b=...

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  13. A binary operation ** is defined on the set of real numbers RR by a**b...

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  14. For the binary operation multiplication modulo 5*(xx(5)) defined on th...

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  15. A binary operation ** on QQ the set of all rational numbers is defined...

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  16. Prove that the identity element of the binary opeartion ** on RR defin...

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  17. Find the identity element of the binary operation ** on ZZ defined by ...

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  18. The binary operation * define on N by a*b = a+b+ab for all a,binN is

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  19. Prove that 0 is the identity element of the binary operation ** on ZZ^...

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  20. A binary operation ** on QQ(0), the set of all non-zero rational numbe...

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