Please help with these true or false questions. Justify answer:)

6. Determine if the following statements are TRUE or FALSE, and justify your answer (e.g. a short proof or counter-example, refer to a theorem, etc). a) (2 points) Consider two n-by-n matrices A, B. For large n, the total operation count of computing the product AB is higher than solving the linear system Ar = b for some vector b using Gaussian elimination and backward substitution. b) (2 points) Any symmetric and invertible n-by-n matrix A has an LU factorization A = LU (that is, without pivoting). I c) (2 points) If the n-by-n matrix A is symmetric, invertible, and has positive diagonal entries (a;; > 0, 1