Matrix Calculator
Perform comprehensive matrix operations including determinant, inverse, transpose, and more
Matrix Operations
Results
Step-by-Step Solution
Example Calculations
2×2 Determinant
Matrix A:
[6 3]
det(A) = 4×3 - 3×6 = -6
Matrix Addition
A + B (element-wise):
[3+6 4+3] = [9 7]
Matrix Operations
Single Matrix
Determinant, trace, inverse, transpose
Operations on one matrix
Two Matrices
Addition, subtraction, multiplication
Operations between matrices
Scalar Operations
Multiply matrix by a number
Scale all elements uniformly
Matrix Properties
Square: Same number of rows and columns
Symmetric: A = A^T (transpose)
Invertible: Non-zero determinant
Diagonal: Non-zero only on diagonal
Identity: Diagonal matrix with ones
Understanding Matrix Operations
What is a Matrix?
A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are fundamental in linear algebra and have applications in computer graphics, engineering, economics, and data science.
Common Operations
- •Determinant: Scalar value indicating invertibility
- •Transpose: Flip matrix across main diagonal
- •Inverse: Matrix that undoes original transformation
- •Trace: Sum of diagonal elements
Matrix Arithmetic
Addition/Subtraction:
C[i,j] = A[i,j] ± B[i,j]
Multiplication:
C[i,j] = Σ(A[i,k] × B[k,j])
Determinant (2×2):
det(A) = a₁₁×a₂₂ - a₁₂×a₂₁
Note: Matrix multiplication is not commutative (A×B ≠ B×A), but addition and subtraction are commutative.