Matrix Calculator (2×2)
Matrix A
Matrix B
A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are fundamental in linear algebra, used for solving systems of equations, 3D computer graphics, machine learning (neural networks), quantum mechanics, and engineering.
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Tip: Matrix multiplication is NOT commutative: AB ≠ BA in general. Always check the order matters for your application.
- 1Matrix addition/subtraction: add corresponding elements (matrices must be same size)
- 2Matrix multiplication: row × column dot products (A must have same columns as B has rows)
- 3Determinant (2×2): det(A) = ad − bc for [[a,b],[c,d]]
- 4Transpose: flip rows and columns (rows become columns)
- 5Inverse (2×2): A⁻¹ = (1/det) × [[d,−b],[−c,a]]
det([[3,8],[4,6]])=−143×6 − 8×4 = 18−32 = −14
[[1,2],[3,4]] × [[5,6],[7,8]]=[[19,22],[43,50]]Row × column products
| Operation | Requirement | Result Size |
|---|---|---|
| Addition (A+B) | Same dimensions | Same as A and B |
| Multiplication (AB) | A cols = B rows | m×p if A is m×n, B is n×p |
| Transpose (Aᵀ) | Any matrix | n×m if A is m×n |
| Determinant | Square matrix only | Scalar |
| Inverse (A⁻¹) | Square, det ≠ 0 | Same as A |
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Fun Fact
The word "matrix" was coined by mathematician James Joseph Sylvester in 1850. In 3D computer graphics, every rotation, scaling, and translation of objects on your screen is performed using matrix multiplication.
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