As a result, the isomorphism classes of CSAs over "K" form a monoid under tensor product, compatible with Brauer equivalence, and the Brauer classes are all invertible: the inverse of an algebra "A" is given by its opposite algebra "A"op (the opposite ring with the same action by "K" since the image of "K" → "A" is in the center of "A"). Explicitly, for a CSA "A" we have "A" ⊗ "A"op = M("n"2, "K"), where "n" is the degree of "A" over "K".