2 × 2 matrix arithmetic
2 × 2 matrix arithmetic: use first matrix · row 1, column 1, first matrix · row 1, column 2, first matrix · row 2, column 1. Review the formula, worked example and calculation steps.
Inputs
Use the units shown—
Enter your values and select Calculate.
Formula & explanation
(AB)ᵢⱼ = Σ Aᵢₖ Bₖⱼ; (A±B)ᵢⱼ=Aᵢⱼ±Bᵢⱼ
Variables & units
- First matrix · row 1, column 1
- Numeric value · minimum -1000000, maximum 1000000
- First matrix · row 1, column 2
- Numeric value · minimum -1000000, maximum 1000000
- First matrix · row 2, column 1
- Numeric value · minimum -1000000, maximum 1000000
- First matrix · row 2, column 2
- Numeric value · minimum -1000000, maximum 1000000
- Second matrix · row 1, column 1
- Numeric value · minimum -1000000, maximum 1000000
- Second matrix · row 1, column 2
- Numeric value · minimum -1000000, maximum 1000000
- Second matrix · row 2, column 1
- Numeric value · minimum -1000000, maximum 1000000
- Second matrix · row 2, column 2
- Numeric value · minimum -1000000, maximum 1000000
- Operation
- Select an option
Worked example
[[1,2],[3,4]] × [[5,6],[7,8]] = [[19,22],[43,50]].
Assumptions
Real 2×2 matrices only. Matrix multiplication is row-by-column and generally not commutative.
Formula version 1.0.0. JavaScript floating-point arithmetic applies. Results display up to 6 decimal places; stored values retain available precision. Use the units shown.
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