What does the superscripted notation in matrix notation mean?

[mcgruff]

This should be a really easy question, but I can't easily find the answer in any of my books. Anyway, in an old test question, the notation...

M¹⁰⁰

...is used. The question gives M as a 3x3 matrix as follows

0 1 0
0 0 1
1 0 0

...and then it asks for M¹⁰⁰.

From the key, I know the answer is still...

0 1 0
0 0 1
1 0 0

...however, I'm not sure what the superscripted notation means. Could someone please fill me in? Thanks.

 

[joeblow]

Multiply M by itself 100 times. What you have is an product of elementary matrices, so it has finite order. That should simplify calculations.

 

[mcgruff]

Multiply M by itself 100 times. What you have is an product of elementary matrices, so it has finite order. That should simplify calculations.

Thanks for the explanation. That makes sense. I feel sort of dumb---I thought it was some notation I hadn't seen before, given that is was three digits for a 3x3 matrix, not simply an exponent.

 

[HallsofIvy]

Actually, you only need to calculate $A^3$. From that you should be able to see what all powers of A are.