Page 66 - DMTH502_LINEAR_ALGEBRA

Linear Algebra

Notes 2. Prove that the four matrices
1 0 1 0 1 0 1 0
, , ,
0 1 0 1 0 1 0 1

form a multiplicative group.
3. If addition and multiplication modulo 10 is defined on the set of integers
R 0, 2, 4, 6, 8 .

Prove that the resulting system is a ring, Is it an integral domain?
4. Prove that the field has no proper ideals.
5. Show that the complex field C is a vector space over the real field R.

1.9 Further Readings

Books I.N. Herstein Topics in Algebra.
Kenneth Hoffman and Ray Kunze, Linear Algebra
Michael Artin, Algebra

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