Consider a matrix A, and let B = rref(A)
(a) Is ker(A) necessarily equal to ker(B)? Explain.
(b) Is im(A) necessarily equal to im(B)? Explain.
The Attempt at a Solution
I feel confident saying yes for (a) and no for (b), and what I can articulate is that (a) is true because the kernel is the augmented matrix with the last column with all zeros, thus, it is irrelevant whether or not the matrix is in rref. But I don't know how to express (b).