please explain step by step that I can totally understand this question, thank you!

Question 2: Let c be a real number and let T: M2x2 + M2x2 be the transformation defined by T(A) = A+c AT where A is a 2 x 2 matrix. (a) Find the image of 5 and 2 under T. 3 Z t (b) Show that T is a linear transformation. (c) Find a basis for Ker T and Ran T when c = -2. (d) Find a basis for Ker T when c is any real number. (Note : There are several cases to consider depending upon the value of c. You may obtain a different answer depending on the value of c.)