Are kernels and images preserved under row reduction?

[Tonyt88]

Homework Statement

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.

Homework Equations

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).

 

[cristo]

What does rref mean?

 

[Tonyt88]

It's reduced row-echelon form, but nevermind, I got the answer, though thanks for the help.