Let A be n n matrix: answer the following questions
(a) What is the condition for matrix A to have inverse? Discuss this in terms of rank, determinant, linear dependence of rows and columns of matrix A, singular or non-singular.
(b) Show that if A has inverse then AT also has inverse
(c) Last class we talked about homogenous linear system. Assume we have n equations with n unknowns, list a condition for this system to have non-trivial solution
(d) rank(A+B) rank(A)+rank(B) give example for 22 matrices for which rank(A+B)would be i. 0 ii. 1 iii. 2