True-False Exercises Jis for a square matrix A. In parts (a)-(1) determine whether the statement is true or false, and justify your answer. (a) If A is a 3 x 3 matrix, then det(2A) = 2 det(A). X (b) If A and B are square matrices of the same size such that det(A) = det(B), then det(A + B) = 2 det(A). X (c) If A and B are square matrices of the same size and A is invertible, then rum alugad det(ABA) = det(B) (d) A square matrix A is invertible if and only if det(A) = 0. Rais e) The matrix of cofactors of A is precisely [adj(A)] F) For every n x n matrix A, we have true (g) If A is a square matrix and the linear system Ax=0 has multiple solutions for x, then det(A) = 0. X (h) If A is ann x n matrix and there exists ann x 1 matrix b such that the linear system Ax = b has no solutions, then the reduced row echelon form of A cannot be I. (i) If E is an elementary matrix, then Ex = 0 has only the trivial solution. (j) If A is an invertible matrix, then the linear system. Ax=0 has only the trivial solution if and only if the linear system Ax=0 has only the trivial solution. (k) If A is invertible, then adj (A) must also be invertible. (1) If A has a row of zeros, then so does adj(A). . A adj(A)=(det(A))/,