please show work and explanation

(b) If the basis for the null space of a 4 x 3 matrix consists of exactly two vectors, how many pivot columns does the matrix have? (c) If X = a b , detX = 2, and Y = c+4a d + 4 a a b , then detY = (d) TA = Ax, where A E R2x2, is a linear transformation that first rotates vectors in R counterclockwise by 7/2 radians about the origin, then reflects them through the x- axis. What is the value of detA