Mathematics

2×2 matrix - formula in LaTeX

A matrix in round brackets. Columns are separated with &, rows with a double backslash. The bmatrix environment gives square brackets and vmatrix the bars of a determinant. All three need the amsmath package.

$$
\begin{pmatrix} a & b \\ c & d \end{pmatrix}
$$

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What the symbols mean

$a, b$

entries of the first row

$c, d$

entries of the second row

A math formula - one of the most frequently typed in assignments, lecture notes and calculus or algebra homework.

Worked example

The determinant of a 2×2 matrix is the product of the main diagonal minus the product of the other one. \det sets the abbreviation upright, like \sin or \log.

Other ways to write it

• Square brackets, common in linear algebra and English-language papers.

  $$\begin{bmatrix} a & b \\ c & d \end{bmatrix}$$

  \begin{bmatrix} a & b \\ c & d \end{bmatrix}

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• The inverse of a 2×2 matrix, provided the determinant ad − bc is nonzero.

  $$A^{-1} = \dfrac{1}{ad - bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$$

  A^{-1} = \dfrac{1}{ad - bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}

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• A small matrix for use inside a sentence, without stretching the line spacing.

  $$\left(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\right)$$

  \left(\begin{smallmatrix} a & b \\ c & d \end{smallmatrix}\right)

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LaTeX commands in this formula

\begin{pmatrix}

matrix in ( )

How to use this formula in LaTeX?

1. Copy the code with the button above - $$…$$ is centered display math.
2. Paste it into the CamteX editor, Overleaf or any LaTeX document.
3. Inside a sentence, use single $…$ instead of double.
4. The formula needs the amsmath package - CamteX templates include it in the preamble.

Related formulas - Mathematics

• System of equations
• Binomial square formulas
• Quadratic formula
• Product rule
• Definite integral