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If A is an n \times n matrix over a ring R satisfying the polynomial identity[x,y][u,v]=0, then an invariant Cayley-Hamilton identity of the form  \Sigma A^{i}c_{i,j}A^{j}=0 with c_{i,j}\in R and c_{n,n}=(n!)^2 holds for A.

Cayley Hamilton theorem with sandwich coefficients for n$\times$n matrices over a ring satisfying [x,y][u,v]=0