# What does a square matrix to the n index mean

I’m working though a textbook and the questions are asking questions using square matrices to the n index. What would this mean in terms of proofs? for example one questions states that two square matrices A and B have the property AB = BA thus prove ABn = BnA

what does the Bn refer to?

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I think you mean ABn=BnAAB^n=B^nA. Then BnB^n is the nnth power of BB — that is nn copies of BB multiplied together, just like raising numbers to powers:
23 means 2×2×2 2^3 \text{ means } 2\times 2\times 2
[1203]3 means [1203][1203][1203] \begin{bmatrix}1&2\\0&3\end{bmatrix}^3 \text{ means } \begin{bmatrix}1&2\\0&3\end{bmatrix}\begin{bmatrix}1&2\\0&3\end{bmatrix}\begin{bmatrix}1&2\\0&3\end{bmatrix}

Nope…book 100% has the n as a subscript not a power…I’m stumped
– Collin McCabe
2 days ago

@CollinMcCabe: Sure it’s not a typo? The claim would actually be true if it were ABn=BnAAB^n=B^nA.
– Henning Makholm
2 days ago