# Invert Command

##### Command Categories (All commands)

Invert[ <Matrix> ]
Inverts the given matrix.
Example: Invert[{{1, 2}, {3, 4}}] yields \mathrm{\mathsf{ \begin{pmatrix}-2 & 1\\1.5 & -0.5\end{pmatrix} }}, the inverse matrix of \mathrm{\mathsf{ \begin{pmatrix}1 & 2\\3 & 4\end{pmatrix} }}.
Note: In the CAS View undefined variables are allowed too.
Example:
Invert[{{a, b}, {c, d}}] yields \mathrm{\mathsf{ \begin{pmatrix}\frac{d}{ad- bc} & \frac{-b}{ad- bc}\\\frac{-c}{ad- bc}& \frac{a}{ ad- bc}\end{pmatrix} }}, the inverse matrix of \mathrm{\mathsf{ \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.
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