Question: Please complete problems 4 and 5 thoroughly and show work! Much appreciated! 5 New ring is nice Let a E Q be a nonzero element

Please complete problems 4 and 5 thoroughly and show work! Much appreciated!

5 New ring is nice Let a E Q be a nonzero element which is not a square (that is, Q). Let Ra be as in the previous exercise. Prove that M1M2 : 0V if and only if M1 = 0v or M2 = 0V. Proof. 4 A new ring Let V = M2(Q) be the ring of 2-by-2 matrices over Q, let a E Q be a nonzero element and define: Ra = span Prove that for all M1, M2 E Ra: MIM2 E Ra MIM2 = M2M1 2 Proof. 0

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