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MatrixMul
Enter two 2×2 matrices — see the product with dot-product steps for each element.
Each element C[i][j] is the dot product of row i of A and column j of B: C[i][j] = Σ A[i][k] × B[k][j]. For 2×2 matrices, each element involves 2 multiplications and 1 addition. Crucially, AB ≠ BA in general — matrix multiplication is not commutative.
Matrix multiplication encodes linear transformations. In graphics, multiplying transformation matrices chains rotations, scales, and translations. In machine learning, neural network layers are matrix multiplications. In economics, input-output models use matrix products to track inter-industry flows.
Matrix A (2x2)
Matrix B (2x2)
A x B
[[19, 22], [43, 50]]
What you entered
C[0][0] = A[0][0]·B[0][0] + A[0][1]·B[1][0]
1×5 + 2×7= 19C[0][1] = A[0][0]·B[0][1] + A[0][1]·B[1][1]
1×6 + 2×8= 22C[1][0] = A[1][0]·B[0][0] + A[1][1]·B[1][0]
3×5 + 4×7= 43C[1][1] = A[1][0]·B[0][1] + A[1][1]·B[1][1]
3×6 + 4×8= 50Result
A x B: [[19, 22], [43, 50]]
Matrix multiplication pairs each row of A with each column of B — unlike addition, it is not commutative, so A x B generally differs from B x A.