Multiplicative Seminorms

Hello,
I'm thining about the following problem:
let R(n,n) be the algebra of nxn real matrices.
Does there exist a "non-trivial" seminorm in R(n,n), such that for every A, B in R(n,n) we have:
||AB||=||A||*||B||? (the "trivial" seminorm is defined by ||A||=0 for every A in R(n,n)).
Thank you very much for your help.
Maury
.

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