Tiling of a $2n \times 2n$ board

Question

Is there a way to tile a $2n \times 2n$ square with dominoes such that two rectangles cannot be partitioned and slide along each other (interlocking)? I was able to show that for $2 \times 2$ and $4 \times 4$ boards, there is no interlocking, but for a $6 \times 6$ grid there were too many options to do via proof by exhaustion. Doing this on an $8 \times 8$ board and so on would be too much, so I was wondering if there were any good ways to approach this?

Answer 1

Example of an interlocking tiling for the $8\times 8$ board.