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Abstract
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Let R be a noncommutative ring with unity and Z(R) be its centre. The
commuting graph of R denoted by (R) is a graph whose vertices
are noncentral elements of R and two distinct vertices x and y are
adjacent if and only if xy = yx. Let F be a finite field. In this paper, we
show that if (R)
∼=
(M3(F)) and Z(R) is a field, then R ∼=
M3(F). In
particular, if (R)
∼=
(M3(Fp)), then R ∼=
M3(Fp).
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