Algebra question plz plz plz help!!!!!!!!!!!!!!!!!?

Question

Does there exist a 2 x 2 matrix A such that ran(A) = ker(A)? if so find A.

Answer 1

I assume ker is the kernel. But what's ran? Rank? That makes no sense. Range?

If it's range, try for a matrix that has both range and kernel being L = {(x,y): x=y}

I think you'll be able to do it. :)

Hint: The conditions on the matrix for each of range or kernel being L are both easy to work out. And they're not inconsistent with each other ...