Solve {ll}{2}&{3}{5}&{4}

$$\begin{bmatrix} \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \end{bmatrix}$$

Calculate Determinant

$$-7$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

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

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

$$2\times 4-3\times 5$$

Multiply 2 times 4.

$$8-3\times 5$$

Multiply 3 times 5.

$$8-15$$

Subtract 15 from 8.

$$-7$$

Evaluate

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