Determinant Multiplication Calculator
This calculator helps you compute the product of determinants of two square matrices. It is ideal for students and professionals working with linear algebra, simplifying determinant multiplication for square matrices of any size.
Determinant Product Solver
Determinant Multiplication Formula
Where:
- $$A$$ and $$B$$ are square matrices of the same size
- $$\det(A)$$ is the determinant of matrix $$A$$
- $$\det(B)$$ is the determinant of matrix $$B$$
- $$\det(C)$$ is the product of their determinants
Determinant Multiplication – Calculation Example
$$A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & 5 \\ 6 & 7 \end{bmatrix}$$
$$\det(A) = (2 \cdot 4) – (3 \cdot 1) = 8 – 3 = 5 $$
$$\det(B) = (0 \cdot 7) – (5 \cdot 6) = 0 – 30 = -30$$
$$\det(C) = \det(A) \times \det(B) = 5 \times (-30) = -150$$
The product of determinants corresponds to the determinant of the product matrix:
$$\det(A \times B) = \det(A) \times \det(B)$$
This property is important in linear algebra and matrix theory, particularly in simplifying matrix product operations. Our calculator ensures accurate and fast determinant multiplication.