Invert Command

Invert[ <Matrix> ]

Inverts the given matrix.

Example: 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}.

Note: In the CAS View undefiened variables are allowed too.

Example:

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.

Example:

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

Note:

The function must contain just one x and no account is taken of domain or range, for example for f(x) = x^2 or f(x) = sin(x).
If there is more than one x in the function another command might help you:

Example:

Both Invert[PartialFractions[(x + 1) / (x + 2)]] and Invert[CompleteSquare[x^2 + 2 x + 1]] yield the inverse functions.

Note: In the CAS View, the command also works if the function contains more than one x.