Isomorphism, informally, means identical structure. The way to show two thingsare notisomorphic is by showing one has a property another does not.

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(i) and (iii) the ring of quaternions is a first example of a strictly skew field. That means the quaternions are not commutative ring. While R x R x R x R is for a direct product of commutative rings.

(i) and (ii) same idea. Matrix multiplication is not commutative.

(ii) and (iii), well, the ring of matrices are not a strictly skew field. In more basic terms, the ring of matrices is not a division ring (not non-zero everything has a multiplicative inverse) while the quaternions are a division ring (everything non-zero has a multiplicative inverse).