True or false: A system comprising two linear equations in two variables has a unique solution if and only if...

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  1. True or false: 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. True or false: 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. True or false: If A and B are matrices of the same order, then .
  4. True or false: If A and B are matrices such that AB and BA are both defined, then A and B must be square matrices.
  5. True or false: If A is a square matrix with inverse and c is a nonzero real number, then .
  6. True or false: If AX = B is a system of n linear equations in n unknowns and does not exist, then AX = B does not have a unique solution.
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