Diagonal matrix - general question

So this is a general matrix question, we are working on inverses. The question ask, for which values of a, b, and c is this matrix invertible?

I said, this matrix is invertible when a = 1, b = 1, c = 1, that would mean this matrix has a rref and thus, it has an inverse. Also, the determinant of this matrix, I believe, is simply: abc. That would mean that a, b and c cannot = 0 by any means, if we want this to be invertible. Is this correct?

if thats the case then the inverse matrix would be...

Is this correct?

Then it asks an even more general question: For which values of the diagonal elements is a diagonal matrix, of arbitrary size, invertible?

Help on this would be much appreciated!