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A binary operation ** is defined on the ...

A binary operation `**` is defined on the set R of real numbers by `a**b={ a, if b = 0, |a|+b,if b!=0` If atleast one of a and b is 0, then prove that `a**b = b**a`. Check whether `**` is commutative. Find the identity element for `**` ,if it exists

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`we have a**b = a if b=0`
`and |a| + b if b cancel(=) 0`
`So, a**b = a, if b=0`
` =b , if a=0`
`so, b**a = b if a=0`
`b**a= a if b=a`
`so, a**b = b**a`
so, `a**b` is commutative
...
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