1. The problem is to find the determinant of a given matrix. 2. The determinant is a scalar value that can be computed from the elements of a square matrix and encodes certain properties of the matrix. 3. For a 2x2 matrix \(\begin{bmatrix}a & b \\ c & d\end{bmatrix}\), the determinant is calculated as \(ad - bc\). 4. For a 3x3 matrix \(\begin{bmatrix}a & b & c \\ d & e & f \\ g & h & i\end{bmatrix}\), the determinant is \(a(ei - fh) - b(di - fg) + c(dh - eg)\). 5. To solve, substitute the matrix elements into the formula and simplify step-by-step. 6. This process can be extended to larger matrices using cofactor expansion or row reduction methods. 7. The determinant helps determine if the matrix is invertible (non-zero determinant) or singular (zero determinant).