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IV. 1. Under matrix addition and multiplication C = $ 6 :0.beR} is a field. i. What is cos 0 - sin 0 sin 0 cos 0 r O ii. Show that D= : r ER ) is a subring of C. r iii. Is D an ideal of C'? 2. A ring R has the property r? = r for each r E R. Show that char R = 2 and R is a commutative ring. 3. List the cosets in the quotient ring 32/9Z. Give the addition and multiplication tables for this ring