jinjin

@ReiAyanami580: Start with basics...

(matrix A) * (vector X) = (vector X)

only when (matrix A) is the identity matrix.

So (matrix A) * (vector X) = k * (vector X)

can only be true when (matrix A) is

k * (identity matrix)

Hence

a, d = k; b, c = 0

The subsitute these values into your equiation and

k^2 - (a+d)k + (ad-bc)=0

becomes

k^2 - 2k^2 + k^2 = 0; 2k^2 - 2k^2 = 0; 0 = 0

And this satifies your other equation:

(matrix A) * (matrix B) = (matrix B) * (matrix C)

because both (matrix A) and (matrix C) are equal to k * (identity matrix)