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1) Let A, B E Rx3 with det(A) = 4 and det(B) = 6, and let E be an elementary matrix of type I.

1) Let A, B E Rx3 with det(A) = 4 and det(B) = 6, and let E be an elementary matrix of type I. Determine the value of each of the following i) det (: A) = ii) det(B-1A") = ii) det(E A2) = %3D 2) If A E R"Xn is nonsingular, show that AT A is nonsingular and det (AT A) > 0.

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