The first forum for Mathematics compatible also with ib mathematics (HL,SL,studies,myp mathematics) - ib math Revision Notes

2 posts
• Page **1** of **1**

IB Mathematics HL Option: Sets, Relations and groups (inverse element)

Let the binary operation on R defined be x*y=x+y+24. Does each element have an inverse element?

Thanks

Let the binary operation on R defined be x*y=x+y+24. Does each element have an inverse element?

Thanks

- elizabeth
**Posts:**0**Joined:**Mon Jan 28, 2013 8:09 pm

IB Mathematics HL Option Sets, relations and Groups - inverse element

The basic principles about iverse element are:

- An element in a set A is an inverse element for an operation * defined over A if

for every element

where e is the identity element.

- For an associative operation *, an element x admits a left-inverse x’and a right-inverse x’’, then these two identities are equal.

- For an operation * on a set A having an identity element then every invertible element admits a unique inverse.

Concerning your question,

First we are going to find the identity element as follows

suppose that y be a right-inverse element of x,

then

The right-inverse element y is also a left inverse of x since

Therefore every element has an inverse of the form

The basic principles about iverse element are:

- An element in a set A is an inverse element for an operation * defined over A if

for every element

where e is the identity element.

- For an associative operation *, an element x admits a left-inverse x’and a right-inverse x’’, then these two identities are equal.

- For an operation * on a set A having an identity element then every invertible element admits a unique inverse.

Concerning your question,

First we are going to find the identity element as follows

suppose that y be a right-inverse element of x,

then

The right-inverse element y is also a left inverse of x since

Therefore every element has an inverse of the form

- miranda
**Posts:**268**Joined:**Mon Jan 28, 2013 8:03 pm

2 posts
• Page **1** of **1**