I have a revision question in my book about matrices but because I learnt it a year ago I can't quite remember all the details so i'll write what I know and hopefully some of you can help me

I have a matrix which is (a,b ; c,d) as in ab on top and cd below and I need to find the conditions on abcd so that it is row equivalent to the identity

For one I know the identity is (1,0 ; 0,1) and im pretty sure the determinant can't be zero in order for it to be row equivalent and equal to the identity but apart from that I don't know the other conditions for it..

The second question is just to check my answer

I have (lamda - 2)x + y = 0

x + (lamda - 2)y = 0

and I have to find the non trivial solutions

In order to do this I find the determinant ( lamda squared + - 4 lamda + 4) then make that equal to zero find the solution for lamda then the non trival solutions are all those except where lamda makes the determinant zero? is that correct?