# What is the determinant of a matrix used for?

Jun 1, 2015

The determinant of a matrix $A$ helps you to find the inverse matrix ${A}^{- 1}$.

You can know a few things with it :

• $A$ is invertible if and only if $D e t \left(A\right) \ne 0$.

• $D e t \left({A}^{- 1}\right) = \frac{1}{D e t \left(A\right)}$

• A^(-1) = 1/(Det(A)) * ""^t((-1)^(i+j)*M_(ij)),

where $t$ means the transpose matrix of $\left({\left(- 1\right)}^{i + j} \cdot {M}_{i j}\right)$,

where $i$ is the n° of the line, $j$ is the n° of the column of $A$,

where ${\left(- 1\right)}^{i + j}$ is the cofactor in the $i$-th row and $j$-th column of $A$,

and where ${M}_{i j}$ is the minor in the $i$-th row and $j$-th column of $A$.