Matrix Squared Calculator
This calculator computes the square of a square matrix by multiplying the matrix by itself. It is useful for students, engineers, and scientists working in linear algebra, computer graphics, and data science.
Matrix Square Solver
Matrix Squaring Formula
$$
C = A^2 = A \times A \\[1em]
C_{ij} = \sum_{k=1}^{n} A_{ik} A_{kj}
$$
Where:
- $$A$$ is a square matrix
- $$C = A^2$$ is the matrix squared (A multiplied by itself)
- $$C_{ij}$$ is the element in row $$i$$, column $$j$$ of the resulting matrix
Matrix Squared – Calculation Example
$$A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$$
$$A^2 = A \times A = \begin{bmatrix} (1 \cdot 1 + 2 \cdot 3) & (1 \cdot 2 + 2 \cdot 4) \\ (3 \cdot 1 + 4 \cdot 3) & (3 \cdot 2 + 4 \cdot 4) \end{bmatrix} = \begin{bmatrix} 7 & 10 \\ 15 & 22 \end{bmatrix}$$
Squaring a matrix is a common operation in linear algebra for analyzing transformations, solving equations, and modeling systems. It requires the matrix to be square. Our calculator simplifies this task by performing matrix multiplication instantly and accurately.