SymPy Gamma

SymPy:

Matrix ([[1,2,3],[4,5,6],[7,8,9]])

$\left[\begin{matrix}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{matrix}\right]$

(Matrix([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])).inv()

$\left[\begin{matrix}1 & 2 & 3\\4 & 5 & 6\\7 & 8 & 9\end{matrix}\right]^{-1} =$

(Matrix([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])).eigenvals()

(Matrix([
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])).eigenvects()

See what Wolfram|Alpha has to say.

Experiment with SymPy at SymPy Live.