Math

Matrix 2×2 Calculator

Determinant and inverse of a 2×2 matrix.

Free to use — no sign-up or login.

Two-by-two matrix transformation plot Matrix column vectors on a Cartesian plane spanning the transformed unit-square parallelogram.

Enter valid values to draw the figure.

col 1 = (a, c) · col 2 = (b, d) · |det| = parallelogram area

Column 1 is (a, c) and column 2 is (b, d); they span a parallelogram whose area is |det|.

Determinant

Inv a

Inv b

Inv c

Inv d

This free Matrix 2×2 Calculator covers Determinant and inverse of a 2×2 matrix.

det = ad−bc; inverse is (1/det) times the adjugate. Related math tools sit beside How it works, with no account required.

Using the Matrix 2×2 Calculator

Determinant and inverse of a 2×2 matrix. Typical inputs are a (1,1), b (1,2), c (2,1) and d (2,2). How it works beside the form states the identity the Matrix 2×2 Calculator applies.

FAQ

How do I use the Matrix 2×2 Calculator?

Open the Matrix 2×2 Calculator, fill a (1,1), b (1,2), c (2,1) and d (2,2), and read the result. Enter a (1,1), b (1,2), c (2,1), and d (2,2) for the Matrix 2×2 Calculator; use finite values in the indicated domain. The calculator reports Determinant, Inv a, Inv b, Inv c, and Inv d: det = ad−bc; inverse is (1/det) times the adjugate. An inverse exists only when Determinant is nonzero.

What formula does the Matrix 2×2 Calculator use?

The Matrix 2×2 Calculator uses the identity in How it works. In words: Enter a (1,1), b (1,2), c (2,1), and d (2,2) for the Matrix 2×2 Calculator; use finite values in the indicated domain. The calculator reports Determinant, Inv a, Inv b, Inv c, and Inv d: det = ad−bc; inverse is (1/det) times the adjugate. An inverse exists only when Determinant is nonzero.