Question

If I have a 2 x matrix to the nth power. What does that mean. I mean let's say n equals 2.

Answer 1

such as \[ A^2 \]?

It means exactly what you think it means. Multiply the matrix by itself 2 times.
\[ A^2 = A A \]
\[ A^3 = A A A \]
etc.

Answer 2

Lets say you have a matrix A, then \(A^2\) mean \(A\timesA\).

Answer 3

\(A\times A\).

Answer 4

notice that raising a matrix to an exponent only makes sense of the matrix is square. Otherwise you can't do the matrix multiplication.