Solve {ccc}{8}&{0}&{4}{5}&{2}&{1}{-1}&{2}&{-1}-{ccc}{4}&{2}&{2}{0}&{-2}&{4}{2}&{-2}&{0}

$$\left( \begin{array} { c c c } { 8 } & { 0 } & { 4 } \\ { 5 } & { 2 } & { 1 } \\ { - 1 } & { 2 } & { - 1 } \end{array} \right) - \left( \begin{array} { c c c } { 4 } & { 2 } & { 2 } \\ { 0 } & { - 2 } & { 4 } \\ { 2 } & { - 2 } & { 0 } \end{array} \right)$$

Evaluate

$$\left(\begin{matrix}4&-2&2\\5&4&-3\\-3&4&-1\end{matrix}\right)$$

Steps Using Rules for Matrix Arithmetic

You can add or subtract two matrices only if both matrices have the same number of rows and columns.

$$\left(\begin{matrix}8&0&4\\5&2&1\\-1&2&-1\end{matrix}\right)-\left(\begin{matrix}4&2&2\\0&-2&4\\2&-2&0\end{matrix}\right)$$

To subtract two matrices, subtract the corresponding elements.

$$\left(\begin{matrix}8-4&-2&4-2\\5&2-\left(-2\right)&1-4\\-1-2&2-\left(-2\right)&-1\end{matrix}\right)$$

Take the difference of each element of the matrix.

$$\left(\begin{matrix}4&-2&2\\5&4&-3\\-3&4&-1\end{matrix}\right)$$

Calculate Determinant

$$68$$