Matrix Calculator
Matrix addition, multiplication, and determinants. Enter values for instant results with step-by-step formulas.
Formula
Det(A) = ad - bc
The determinant of a 2x2 matrix is the product of the main diagonal minus the product of the other diagonal.
Worked Examples
Example 1: Determinant
Problem:Find Det of [[1, 2], [3, 4]]
Solution:(1)(4) - (2)(3) = 4 - 6 = -2
Result:-2
Example 2: Addition
Problem:[[1,2],[3,4]] + [[1,1],[1,1]]
Solution:Add elements: 1+1, 2+1...
Result:[[2,3],[4,5]]
Frequently Asked Questions
Is matrix multiplication commutative?
Generally, no. A × B is usually not equal to B × A. Order matters.
What is the identity matrix?
A square matrix with 1s on the main diagonal and 0s elsewhere. Multiplying by it leaves a matrix unchanged (AI = A).
What is an Inverse Matrix?
The inverse (A⁻¹) is a matrix that, when multiplied by the original matrix A, yields the Identity matrix.
What is a singular matrix?
A matrix that does not have an inverse. This happens when its determinant is zero.