Determinants

Summary

• The determinant of a $2×2$ matrix

$$A=\begin{bmatrix}a & b\\c & d\end{bmatrix}$$

• is denoted by $|A|$ or $det(A)$ and it is defined as the real number

$$\left| A \right|=ad-cb$$

• The determinant for a square $n×n$ matrix $A$ , $|A|$ or $det(A)$ , is also a real number (exactly how it is calculated is not part of this lecture).
• If $A$ is not a square matrix, it has no det erminant.
• Result: A square $n×n$ matrix $A$ is invertible if and only if $|A|≠0$ .