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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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Answer» `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 `**` is a commutative identity element `a**e = a ` `a**e = e , if a=0` `and a**e= a if e=0` `so, a**e= a` so, identity element e=0 |
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