Matrix Calculator

Perform matrix operations: addition, subtraction, multiplication, determinant, and transpose for 2x2 matrices.

This calculator performs one of five 2×2 matrix operations — Addition, Subtraction, Multiplication, Determinant, or Transpose — selected by the Operation dropdown (lines 25-52), computing only the operation you've chosen. At the default Addition operation, each result cell is a simple sum of the matching cells from Matrix A and Matrix B — Result [1,1] = a11 + b11 (line 27) — so Matrix B's element shows a larger measured sensitivity than Matrix A's matching cell, purely because Matrix B's default values (5-8) are larger numbers than Matrix A's (1-4); the addition formula itself weighs both cells identically. Determinant of A is only actually computed when Operation is set to 4 (lines 43-45) — at every other Operation setting, including the default Addition, it stays fixed at its initialized value of 0 (line 22) regardless of what any of the eight matrix elements are set to, which can read as "this matrix has a zero determinant" when really the calculator simply hasn't computed it. Trace, unlike the other outputs, is computed unconditionally regardless of Operation (line 55) and depends only on a11 and a22 — Matrix B's four elements never affect it at all. This calculator does not support matrices larger than 2×2, and it does not compute a matrix inverse as an output — the How to Use notes describe the formula for one, but no inverse value ever appears among the calculator's actual results.