# INV matrix function

## Description

INV(**A**) Returns the inverse matrix for the square matrix **A**.

The **inverse** *A ^{−1}* of a square matrix

*A*is the unique matrix such that:

$$ A^{-1}A = I = AA^{-1} $$

That is, the inverse of *A* is the matrix *A ^{−1}* that you have to multiply

*A*by in order to obtain the identity matrix

*I*.

Note that when the argument of the INV function is a real number x, then INV(x) returns x^{−1} or 1/x, so that analogously:

$$ x^{-1}x = 1 $$

To invert all elements of a matrix *A*, use the function POWER(*A*,-1).

## Calculator

## See also

## Recommended book

## Matrix Algebra Useful for Statistics

Shayle R. Searle, Andre I. Khuri

Buy from Amazon

This book addresses matrix algebra that is useful in the statistical analysis of data as well as within statistics as a whole. The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained.