Solve Matrix

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

Calculate Determinant

$$-2$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

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

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

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

Multiply 5 times 2.

$$10-3\times 4$$

Multiply 3 times 4.

$$10-12$$

Subtract 12 from 10.

$$-2$$

Evaluate

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