I am trying to implement a 2D isometric game, well diametral with a pixel ratio of 2: 1. The problem is that the rotation matrix that I made does not seem to work. It is a bit off and does not line up:

I'm not sure if I made my rotation matrix correctly:

$$

begin {bmatrix}

1 / sqrt {2} & 0 & -1 / sqrt (2) \

1 sqrt {10} & 2 / sqrt {5} & -1 / sqrt {10} \

-1 sqrt {2/5} & 1 / sqrt {5} & sqrt {2/5} \

end {bmatrix}

$$

For the angles I used 45 degrees and arctan (1/2) which is approximately 26.5 degrees. I need the 3 axes, since I'm using lights and I need the tiles to have depth.