Question

The center of the ring S of all 2×2 matrices over a field F consists of all matrices of the form ( a 0 )

( 0​ a​ )

Answer 1

The center of the ring S consists of all matrices with a specific form.

Step-by-step explanation:

The question is asking about the center of the ring S, which consists of all 2x2 matrices of a specific form. To find the center of this ring, we need to identify the matrices that satisfy the given form.

The matrices in the center of the ring have the form:

( a 0 )
( 0​ a​ )

Where 'a' represents any element from the field F. These matrices have the same value 'a' along the main diagonal, and zeros in all other positions. This is the definition of the center of the ring S.