Please solve

6. Explain why or why not Determine whether the following statements are true and give an explanation or counterexample (a) Let A and B be matrices such that the product is defined. If B has a column of zeros, then so does AB (b) A system of 2 equations in 3 unknowns that has x = 1, y = 2, z = -1 as a solution must then have infinitely many solutions (c) If A and B are 4x6 matrices, then the multiplication BAT is well defined (d) If there is a path C for which S F . dr = 0 then F must be a conservative field (e) The vector field F = has both zero circulation along and zero flux across the unit circle centered at the origin