I have to proove that a singular (2 x 2)-matrix can be written as a b ta tb or ta tb a b My attempt is not a real proof, and as I'm very inexperienced with writing proofs, maybe someone could write it, so that I will understand it in the future. Attempt. Let B = a b c d From the definition, det(B)= ad-bc. For a singular matrix, det(B) = 0. Hence ad-bc=0 <=> ad=bc <=> a/c=b/d. We have that one row is a multiple of the other. If A= a b ta tb then we have a/ta=b/tb <=> 1/t=1/t, and that's true for all real t > 0. And if A = ta tb a b Then we have ta/a=tb/b <=> t=t, which is true for all t,a,c.