Invert Command

Invert( <Matrix> ): Inverts the given matrix.

Invert({{1, 2}, {3, 4}}) yields \(\begin{pmatrix}-2 & 1\\1.5 & -0.5\end{pmatrix}\), the inverse matrix of \(\begin{pmatrix}1 & 2\\3 & 4\end{pmatrix}\).

In the CAS View undefined variables are allowed too.

Invert({{a, b}, {c, d}}) yields \(\begin{pmatrix}\frac{d}{ad- bc} & \frac{-b}{ad- bc}\\\frac{-c}{ad- bc}& \frac{a}{ad- bc}\end{pmatrix}\), the inverse matrix of \(\begin{pmatrix}a & b\\c & d\end{pmatrix}\).

Invert( <Function> ): Gives the inverse of the function.

Invert(sin(x)) yields asin(x).

No account is taken of domain or range, for example for f(x) = x² or f(x) = sin(x).
The command works faster for functions that only contain one x. To make your construction more efficient you may want to rearrange your functions and use eg NInvert((x+1)^2-1) rather than NInvert(x^2+2x).
See also NInvert Command, Eigenvalues Command, Eigenvectors Command, SVD Command, Transpose Command, JordanDiagonalization Command