8. Determine whether each statement is true or false, and provide a justification or a counterexample. (a) (3 points) If A is an n x n matrix such that |Av| | = |7| for every 7 6 R", then there exists some b e R" such that the system of linear equations Ar = b has infinitely many solutions. (b) (3 points) If A is an m x n matrix and B = rref(A), then ker(A) = ker(B). (c) (3 points) If A is an orthogonal matrix, there exists an orthonormal basis of eigenvectors for A. (d) (3 points) If A and B are matrices whose eigenvalues, counted with their algebraic multiplicities, are the same, then A and B are similar