Matrix Calculator — Add, Subtract, Multiply & Find Determinant

Perform matrix addition, subtraction, multiplication, and scalar multiplication — plus calculate the determinant and transpose of any matrix up to 4×4 in size. Matrix operations are the foundation of linear algebra, computer graphics, machine learning, and engineering simulations. This calculator handles all core operations with clean output and shows key properties of each result: determinant, rank, whether the matrix is symmetric or singular. The determinant is especially important: a determinant of zero means the matrix is singular — it has no inverse, meaning the system of equations it represents has no unique solution. In practical terms, a singular matrix means you cannot solve the underlying linear system uniquely — critical in structural engineering and regression analysis. Matrix multiplication follows strict dimension rules: an m×n matrix times an n×p matrix yields an m×p result. This calculator validates dimensions automatically and explains any mismatch. The transpose operation flips a matrix across its diagonal — a common step in statistics and graphics transformations.