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Maths-

General

Easy

Question

If (G,×) is a group such that $left parenthesis a cross times b right parenthesis squared equals left parenthesis a cross times a right parenthesis cross times left parenthesis b cross times b right parenthesis$ for all $a comma b cross times G comma$ then G is

Abelian
Finite
Infinite
None of these

The correct answer is: Abelian

$left parenthesis a cross times b right parenthesis squared equals left parenthesis a cross times a right parenthesis cross times left parenthesis b cross times b right parenthesis text for all end text a comma b element of G$
$rightwards double arrow left parenthesis a cross times b right parenthesis cross times left parenthesis a cross times b right parenthesis equals left parenthesis a cross times a right parenthesis cross times left parenthesis b cross times b right parenthesis text for all end text a comma b element of G$
$rightwards double arrow a cross times left parenthesis b cross times a right parenthesis cross times b equals a cross times left parenthesis a cross times b right parenthesis cross times b text for all end text a comma b element of G$
$rightwards double arrow b cross times a equals a cross times b text for all end text a comma b element of G$
G is abelian.

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parallel

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parallel

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