2x2 Matrix Addition Calculator

About this calculator

Adding two 2×2 matrices is entry-by-entry addition: each position in the result matrix is simply the sum of the two numbers sitting in that same position in the original matrices. Unlike matrix multiplication, matrix addition is commutative and only works when both matrices have identical dimensions, since every entry needs a matching partner to add to.

Matrix addition is the basic building block underneath far more complex operations: it is how you combine forces or displacement vectors stacked into matrix form in physics and engineering, how you superimpose two linear transformations in computer graphics, and how systems of linear equations get manipulated when solving them with matrix methods. Small 2×2 cases like this are exactly where students first practice the rules before moving to larger matrices.

Enter the four entries of each 2×2 matrix and this calculator adds them together, showing the resulting matrix.