Matrix Multiplication Calculator
Multiply two 2x2 matrices. Enter the elements of A and B to compute C = A * B.
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Request a ToolHow to Use the Matrix Multiplication Calculator
Enter the elements of two 2x2 matrices (A and B) and the calculator computes the product C = A * B.
- Enter Matrix A. Fill in all four elements of the first matrix.
- Enter Matrix B. Fill in all four elements of the second matrix.
- Read the result. The product matrix C appears with each element shown individually.
Matrix multiplication follows the rule: c_ij = sum of a_ik * b_kj. For 2x2 matrices, each element of C is the dot product of the corresponding row of A and column of B.
About Matrix Multiplication
Matrix multiplication is a core operation in linear algebra. Unlike scalar multiplication, it is not commutative (A*B does not always equal B*A). It is used in computer graphics for transformations, in physics for rotations, in economics for input-output models, and in machine learning for neural network computations. The product of two 2x2 matrices is always a 2x2 matrix.
Frequently Asked Questions
How do you multiply two 2x2 matrices?
Each element of the product is the dot product of a row from the first matrix and a column from the second. For example, c11 = a11*b11 + a12*b21.
Is matrix multiplication commutative?
No. In general, A*B is not equal to B*A. The order of multiplication matters in matrix algebra.
When can you multiply two matrices?
You can multiply matrix A (m x n) by matrix B (p x q) only if n = p (the number of columns in A equals the number of rows in B). The result is an m x q matrix.