Determinante
Teorema (Laplasova teorema):
Ako je $D= |a_{ij}|$ tada je:
(1) $D= \begin{vmatrix} a_{11} & a_{12} & ...& a_{1n}\\ a_{21} & a_{22} & ...& a_{2n}\\ . & . & ...& .\\ . & . & ...& .\\ . & . & ...& .\\ a_{n1} & a_{n2} & ...& a_{nn} \end{vmatrix} = \displaystyle \sum_{i=1}^n a_{ij}A_{ij}; D=a_{1j}A_{1j} +a_{2j}A_{2j} +...+a_{nj}A_{nj}$,
razvoj po $i$-toj koloni .
(2) $D= \begin{vmatrix} a_{11} & a_{12} & ...& a_{1n}\\ a_{21} & a_{22} & ...& a_{2n}\\ . & . & ...& .\\ . & . & ...& .\\ . & . & ...& .\\ a_{n1} & a_{n2} & ...& a_{nn} \end{vmatrix} = \displaystyle \sum_{j=1}^n a_{ij}A_{ij}; D=a_{i1}A_{i1} +a_{i2}A_{i2} +...+a_{in}A_{in}$,
razvoj po $j$-toj vrsti.