Let A € M₂ (R) be given. (a) If AA¹ = 0n, prove that A = On. Does this hold if A € M₂(C)? (b) Suppose that A¹A = AA¹. Prove that A¹A = A² if and only if A is symmetric.

Q: assume that Pr[A′]=0.55, Pr[B]=0.35 , and Pr[A′∩B]=0.2. (1) Pr[A∩B]=Pr[A∩B]=   (2)…

A: Solution : Given information; P(A')=0.55 P(A)=1-P(A')=0.45P(B)=0.35 and P(A'∩B)=0.2

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