Matrix Calculator
Compute 2×2 linear algebra operations including determinant, multiplicative inverse, matrix addition, subtraction, multiplication, and matrix trace.
Top-left element of Matrix A
Top-right element of Matrix A
Bottom-left element of Matrix A
Bottom-right element of Matrix A
Choose matrix transformation or binary operator
Top-left element of Matrix B
Top-right element of Matrix B
Bottom-left element of Matrix B
Bottom-right element of Matrix B
Computed matrix, determinant, or scalar output
How to Use This Calculator
- Enter elements for Matrix A.
- Select the desired linear algebra operator (det, inverse, add, subtract, multiply).
- Enter elements for Matrix B if performing binary operations.
- Review the computed matrix, determinant, and trace.
Formula & Calculation Methodology
The determinant of a 2×2 matrix equals the product of diagonal elements minus anti-diagonal elements. The inverse swaps diagonal terms and negates off-diagonals.
Worked Example
Determinant of Matrix A [[4, 7], [2, 6]]
Multiplying Matrix A [[1, 2], [3, 4]] by Identity B [[1, 0], [0, 1]]
Frequently Asked Questions
What occurs when the determinant is zero?↓
A matrix with a determinant of zero is called singular. Singular matrices do not possess a multiplicative inverse because division by zero is impossible.
Is matrix multiplication commutative (A × B = B × A)?↓
No. In linear algebra, matrix multiplication is non-commutative in the general case: A × B rarely equals B × A.
What is the trace of a matrix?↓
The trace tr(A) is the sum of the elements along the main diagonal (from top-left to bottom-right). It equals the sum of the eigenvalues.
What is a geometric interpretation of the determinant?↓
In two dimensions, the absolute value of the determinant represents the area of the parallelogram formed by the row (or column) vectors.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.