Why E's representation marix is unit matrix

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In group representation theory, identity element's representation matrix is unit matrix. But why? Could you give me an exact explanation? Thany you.
 
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Group representation theory essentially boils down to using matrices to represent group elements. In other words, a group is described as a set of linear transformations on vector spaces. In this respect it is obvious that the identity element will be the identity matrix.
 
I know this, but I don't know how to prove that exactly
 
The group identity has the property that ae= a and ea= a for any group member a. Suppose e is "represented" by the matrix E and a by the matrix A. Then you must have AE= A and EA= A, for any matrix, A, in the group representation. Therefore E= ?
 

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