True or False. Justify your answer.

1) If A is square and Ax = b is inconsistent for some b, then A is not invertible.

2) The reduced row echelon form of any 4 x 2 matrix has at least 6 zeroes.

3)Any set of three vectors in R²is linearly dependent.

4) If A is right invertible, then Ax = 0 has a unique solution.

5) Prove that if A is a square matrix and invertible, then so is A³. (Extra credit: prove that if A³is invertible, then so is A.)

6) Prove that if A is a square matrix then A + A^Tis symmetric.