Abstract
Let Mn(D) be the ring of all n×n matrices over a division ring D, where n≥2 is an integer and let GLn(D) be the set of all invertible matrices in Mn(D). We describe maps f:GLn(D)→Mn(D) such that [f(x),f(y)]=[x,y] for all x,y∈GLn(D). The analogous result for singular matrices is also obtained.
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