Solve {cc}{omega}&{omega}{-1}&{omega}

$$\left| \begin{array} { c c } { \omega } & { \omega } \\ { - 1 } & { \omega } \end{array} \right|$$

Evaluate

$$\omega \left(\omega +1\right)$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

$$det(\left(\begin{matrix}\omega &\omega \\-1&\omega \end{matrix}\right))$$

For the 2\times 2 matrix \left(\begin{matrix}a&b\\c&d\end{matrix}\right), the determinant is ad-bc.

$$\omega \omega -\omega \left(-1\right)$$

Multiply \omega times \omega .

$$\omega ^{2}-\omega \left(-1\right)$$

Multiply \omega times -1.

$$\omega ^{2}-\left(-\omega \right)$$

Subtract -\omega from \omega ^{2}.

$$\omega \left(\omega +1\right)$$

Integrate w.r.t. ω

$$\frac{\omega ^{3}}{3}+\frac{\omega ^{2}}{2}+С$$