This is really intriguing topic, and fondly brings back mathematical techniques that I probably haven't used in decades. What fun!

Squaring

0 1
2 3
[download]

does give

2  3
6 11
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and multiplying it again produces

 6 11
22 39
[download]

(I'm sure there's a good reason why the top row of the cube has the same values as the bottom row of the square.) The module I suggested doesn't provide a power function, so I suppose the developer would have to jerry-rig something up that multiplies a matrix by itself n-1 times.