🔲 Matrix Calculator
Perform matrix operations with step-by-step solutions
Matrix A
Matrix B
Result
Step-by-step calculation
- 1.A = [[0, 0], [0, 0]]
- 2.B = [[0, 0], [0, 0]]
- 3.A + B: add corresponding elements
- 4.C[1][1] = 0 + 0 = 0
- 5.C[1][2] = 0 + 0 = 0
- 6.C[2][1] = 0 + 0 = 0
- 7.C[2][2] = 0 + 0 = 0
How Matrix Calculations Work
- 1Enter matrix dimensions and values.
- 2Select the operation: add, subtract, multiply, transpose, determinant, or inverse.
- 3For addition/subtraction: matrices must have the same dimensions.
- 4For multiplication: columns of matrix A must equal rows of matrix B.
- 5The calculator performs the operation and shows step-by-step work.
About Matrix Calculator
Perform matrix operations: addition, subtraction, multiplication, transpose, determinant, and inverse. Supports 2×2, 3×3, and custom-sized matrices with step-by-step solutions.
Frequently Asked Questions
What is a matrix determinant?
The determinant is a scalar value calculated from a square matrix. For 2×2: det = ad − bc. It indicates whether the matrix is invertible (det ≠ 0) and represents the scaling factor of the linear transformation.
When is matrix multiplication possible?
Matrix A (m×n) can multiply matrix B (p×q) only if n = p (columns of A = rows of B). The result has dimensions m×q. Matrix multiplication is not commutative: A×B ≠ B×A in general.
What is a matrix inverse?
The inverse of matrix A (written A⁻¹) satisfies A × A⁻¹ = I (identity matrix). Only square matrices with non-zero determinants have inverses. It's used to solve systems of linear equations.