## 1.3 The Inverse of a Matrix

### The Determinant of a 2×2 Matrix

- The
**determinant**of a**2 x 2 matrix**can be calculated as:

\text { det }=A_{1,1} A_{2,2}-A_{1,2} A_{2,1}

- The
**determinant**of an**identity matrix**is equal to**1**.

Example

A=\left[\begin{array}{ll} 1 & 2 \\ 3 & 4 \end{array}\right]

The determinant of the above matrix is:

\operatorname{det}=1 * 4-2 * 3=-2