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set of all invertible diagonal matrices

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Let R be any ring with identity 1 and GL(n, r) the group of invertible nxn matrices over R and SL(n, R) those matrices of determinant 1.
1) Show that SL(n, R) forms a normal subgroup of GL(n, R)
2) Define a group of homomorphism fronm GL(n, R) to another group for which SL(n, R) is the kernel
3) Determine the center of the group GL(n, R). (Describe those invertible matrices that commute with all over invertible matrices)

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A set of all invertible diagonal matrices is depicted.

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Proof:
(1) I claim that .
For any matrix , we have from the definition. Now for any , we have

Thus ...

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