(ab) det(A) = ad-bc. a. Prove that the column vectors of the matrix A are linearly...

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(ab) det(A) = ad-bc. a. Prove that the column vectors of the matrix A are linearly independent if and only if det(A) = 0. b. Prove that the row vectors of the matrix A are linearly independent if and only if det(A) = 0. c. Prove that the column vectors of the matrix A are linearly independent if and only if the row vectors of the matrix A are linearly independent. 5. The determinant of the 2 x 2 matrix A = is (ab) det(A) = ad-bc. a. Prove that the column vectors of the matrix A are linearly independent if and only if det(A) = 0. b. Prove that the row vectors of the matrix A are linearly independent if and only if det(A) = 0. c. Prove that the column vectors of the matrix A are linearly independent if and only if the row vectors of the matrix A are linearly independent. 5. The determinant of the 2 x 2 matrix A = is