Solve {cc}{-2}&{3}{-4}&{5}

$$\left( \begin{array} { c c } { - 2 } & { 3 } \\ { - 4 } & { 5 } \end{array} \right)$$

Calculate Determinant

$$2$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

$$det(\left(\begin{matrix}-2&3\\-4&5\end{matrix}\right))$$

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

$$-2\times 5-3\left(-4\right)$$

Multiply -2 times 5.

$$-10-3\left(-4\right)$$

Multiply 3 times -4.

$$-10-\left(-12\right)$$

Subtract -12 from -10.

$$2$$

Evaluate

$$\left(\begin{matrix}-2&3\\-4&5\end{matrix}\right)$$