1. The problem is to find a 3 by 3 matrix for which you can calculate its inverse. 2. A matrix must be square (same number of rows and columns) and have a non-zero determinant to have an inverse. 3. Let's consider the matrix $$A = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0 \end{bmatrix}$$. 4. This matrix is 3 by 3 and its determinant is calculated as: $$\det(A) = 1 \times (1 \times 0 - 4 \times 6) - 2 \times (0 \times 0 - 4 \times 5) + 3 \times (0 \times 6 - 1 \times 5)$$ 5. Simplifying the determinant: $$\det(A) = 1 \times (0 - 24) - 2 \times (0 - 20) + 3 \times (0 - 5) = -24 + 40 - 15 = 1$$ 6. Since the determinant is 1 (non-zero), matrix $A$ is invertible. 7. You can now calculate the inverse of matrix $A$ using the formula for the inverse of a 3x3 matrix or other methods like row reduction. This matrix is suitable for your inverse calculation practice.