|
- The identity element of s group is unique.
- The inverse of each element of a group is unique, i.e., in a group
 with operation for every , there is only element  such that ,  being the identity.
- The inverse
 of , then the inverse of  is  , i.e.,  .
- The inverse of the product of two elements of a group
 is the product of the inverse taken in the inverse order i.e. .
- Cancellation laws holds in a group, i.e., if
 are any elements of a group , then  (left cancellation law),  (right cancellation law).
- If
 is a group with binary operation and if  and  are any elements of , then the linear equations  and  have unique solutions in .
- The left inverse of an element is also its right inverse, i.e.
 . |
