Is it possible to contruct a 4x3 matrix b and a 3x4 matrix c such that bc is invertible?

Which expression is equivalent to the expression below? (6c^2 + 3c) / (-4c + 2) / (2c + 1) / (4c - 1)a. 3c(2c-1) / (2c + 1)b. -3c(2c-1)^2 / (2c + 1)^2c. 3cd. -3c(just took the test its d. -3c)

The investigating team suspected that there were differences in the cost of repairing cars in workshop i and workshop ii. the investigating team suspected that the costs raised by workshop i were greater than workshop ii. for that they tested the repair of 15 cars in each workshop to see the cost of repairs.the decision of the right hypothesis to prove the suspicion above is a. h0 : μ1- μ2­ = 0; ha : μ1- μ2­ ≠ 0 b. h0 : μ1- μ2 ≥ 0; ha : μ1- μ2 < 0 c. h0 : μd ≥ 0; ha : μd < 0 with μd = μ2- μ1 d. h0 : μd = 0; ha : μd ≠ 0 with μd = μ2- μ1 e. h0 : μ1- μ2 = 0; ha : μ1- μ2 ≥ 0

Let f(x) = x + 2 and g(x) = x2 + 4. find f(g(f(