Problem 3 . Find the matrix A that solves the equation [} 0&2&1 0&0&-1 2&1&0

To solve the given matrix equation, we need to find the matrix A that satisfies the equation: First, let's rewrite the equation in a more standard form: Now, we can solve for matrix A by multiplying both sides of the equation by the inverse of the matrix on the left-hand side: To find the inverse of the matrix , we can use the following formula: where is the determinant of the matrix .Calculating the determinant, we get: Now, we can calculate the inverse of the matrix : Finally, we can substitute the inverse matrix and the given matrix into the equation for A: Simplifying the right-hand side, we get:$A = \frac{1}{2} \cdot [\begin{matrix} 0&-2&1\\ 0&2&1\\ -2&1&0\end{matrix} ] \cdot [\begin{matrix} 1&2&3\\ 3&2&1\\ 1&2&-1\end{matrix} ] - \frac{1}{2} \cdot [\begin{matrix} 0&-2&1\\ 0&2&1\\ -2&