## Abstract

Let *K* be any field, let *L _{n}* denote the Leavitt algebra of type (1,

*n*– 1) having coefficients in

*K*, and let M

*(*

_{d}*L*) denote the ring of

_{n}*d*×

*d*matrices over

*L*. In our main result, we show that M

_{n}*(*

_{d}*L*) ≅

_{n}*L*if and only if

_{n}*d*and

*n*– 1 are coprime. We use this isomorphism to answer a question posed in [

*W. Paschke*and

*N. Salinas*, Matrix algebras over , Michigan Math. J.

**26**(1979), 3–12.] regarding isomorphisms between various C*-algebras. Furthermore, our result demonstrates that data about the

*K*

_{0}structure is sufficient to distinguish up to isomorphism the algebras in an important class of purely infinite simple

*K*-algebras.

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