Can you tile a chessboard with two missing squares?

If you remove two opposite corners of a chessboard, can you still tile it with 2 x 1 rectangles?

In other words, looking at the image above,
can you cover the whole chessboard with 2 x 1 domino tiles,
*except* for the top-left and bottom-right corners?

Congratulations to the ones that solved this problem correctly and, in particular, to the ones who sent me their correct solutions:

- David H., Taiwan;
- Kees de L., Netherlands;

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