Question: Determine whether the given statement is true or false, and give a justification for your answer. (a) IfAis annnmatrix with det(A3In) = 0, then there

Determine whether the given statement is true or false, and give a justification for your answer.

(a) IfAis annnmatrix with det(A3In) = 0, then there is a vectorvRnsuch thatAv= 3v.

(b) IfA+B=In,thendet(A)+det(B)=0ordet(A)+det(B)=1. (c) For every 22 matrixA, there is a 22 matrixBwithB2=A.

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