2×2 matrix determinant

Client

Compute det [[a,b],[c,d]] from four numbers—linear algebra helper in your browser.

-2

Nearby workflows on Toolcore

  • Slope from coordinates — Paste x1,y1 x2,y2 to get line slope. when units or numeric output should be checked on a related calculator.
  • Math expression evaluator — Evaluate basic + − × ÷ arithmetic with parentheses in your browser—no variables. when units or numeric output should be checked on a related calculator.
  • Quadratic equation solver — Solve ax² + bx + c = 0 with discriminant—real or complex roots, computed in your browser. when units or numeric output should be checked on a related calculator.
  • Combinations & permutations — Calculate nCr and nPr for counting problems—BigInt combinatorics in your browser. when units or numeric output should be checked on a related calculator.

About this tool

Quick determinant for 2×2 matrices—first step in checking invertibility or solving small linear systems.

Common use cases

  • Verify det steps in introductory linear algebra homework.
  • Check whether a 2×2 transform preserves orientation (sign of det).

Common mistakes to avoid

  • Wrong entry order

    Order is row-major: a b on top row, c d on bottom.

FAQ

3×3 matrices?

This page is 2×2 only—use a CAS for larger matrices.

Zero determinant?

Det 0 means the matrix is singular (not invertible).

More tools

Related utilities you can open in another tab—mostly client-side.