Determinant

Definition

Let $A\in R^{n\times n}$ or $\in C^{n\times n}$. Then the determinant of $A$, denoted by $\det A$ can be computed on the first row by:

$$\det A=\sum _{j=1}^n(-1{)}^{j-1}{a}_{1j}\det A_{1j}$$ $$\det A=\sum _{j=1}^n(-1{)}^{j-1}{a}_{ij}{M}_{ij}$$

where $M_{ij}$ is the minor.