True or False

1. A system comprising two linear equations in two variables has a unique solution if and only if the straight lines represented by the equations are nonparallel.

2. Suppose the straight lines represented by a system of two linear equations in two variables are parallel to each other. Then the system has infinitely many solutions.

3. If A and B are matrices of the same order, then (A+B)^T = A^T + B^T .

4. If A and B are matrices such that AB and BA are both defined, then A and B must be square matrices.

5. If A is a square matrix with inverse A^-1 and c is a nonzero real number, then (cA) ^-1 =1/c(a ^-1 ) .

6. If AX = B is a system of n linear equations in n unknowns and a ^-1 does not exist, then AX = B does not have a unique solution.