I have to show 0= T(A)=A+A^T

A=[a b].

///[c d]

I got it to where [2a c+b]=[0 0]

///////////////////[b+c 2d]//[0 0]

I know a=d=0 and b=-c. but then i can seem to figure out why the answer is

ker T={[0 -b]

////////[b 0] where b is a real number}

how do they get that?