2x2 Matrix Multiplication Calculator
Multiply two 2x2 matrices together.
Enter matrix values and get the product matrix instantly.
Product Matrix
Matrix multiplication combines two matrices to produce a new matrix.
For two 2×2 matrices A and B, the product C = A × B is:
A = [a b] B = [e f] C = [ae+bg af+bh]
[c d] [g h] [ce+dg cf+dh]
Example:
[1 2] × [5 6] = [1×5+2×7 1×6+2×8] = [19 22]
[3 4] [7 8] [3×5+4×7 3×6+4×8] [43 50]
Key rules:
- Matrix multiplication is not commutative: A × B ≠ B × A (usually)
- Matrix multiplication is associative: (A × B) × C = A × (B × C)
- The identity matrix I = [[1,0],[0,1]] gives A × I = A