I was trying to do something like a general formula, and testing, I came with this:
$ \left( \begin{array}{cc} a & b \\ a' & b' \\ \end{array} \right)^2=\left( \begin{array}{ccc} a^2+a'b & b(a+b') \\ a'(a+b') & b'^2+a'b \\ \end{array} \right) $
I've also tried with a $3$x$3$ matrix, but i don't get anything.
I was trying to do something that can solve matrices like this with only one formula:
$ \left( \begin{array}{ccccc} a_{11}&a_{12}&a_{13}&…&a_{1j}\\ a_{21}&a_{22}&a_{23}&…&a_{2j}\\ a_{31}&a_{32}&a_{33}&…&a_{3j}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ a_{i1}&a_{i2}&a_{i3}&\dots&a_{ij} \end{array} \right)^{n} $
And that's what I want to know.