2. Define = {(9₂2) = 0,²€c} : a, Bec}; (i) Prove MH is a subring of Mat2 (C) with usual matrix addition and multiplication. (ii) Prove it is a division ring. (iii) Prove it is non-commutative. (iv) Prove that the matrix product in MH reflects the product of quaternions described in class. (v) Find a linearly independent set of generators of MH as an R-vector space. MH

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