2x2 Determinants

Simple overview of the formula for finding the determinant of $2\times 2$ matrices.

$2\times 2$ Matrix Determinant Formula

For a $2\times 2$ matrix

\[A= \begin{bmatrix} a & b \\ c & d \end{bmatrix}\]

the determinant is

\[\det(A)= \begin{vmatrix} a & b \\ c & d \end{vmatrix} =ad-bc\]

Watch this section: the general $2\times 2$ determinant formula at 0:30.

First Example

Consider

\[\begin{vmatrix} 2 & 5 \\ 3 & 9 \end{vmatrix}\]

The down-right diagonal gives (includes top-left value and bottom-right value, the “main diagonal”)

\[2\cdot 9=18\]

The other diagonal gives (includes top-right value bottom-left value)

\[5\cdot 3=15\]

Now subtract

\[\begin{vmatrix} 2 & 5 \\ 3 & 9 \end{vmatrix} =2\cdot 9-5\cdot 3 =18-15 =3\]

Watch this section: the thumbnail example at 0:00.

Timestamp Guide

Section	What is shown	Video
Opening example	Start with a concrete $2\times 2$ determinant.	0:00
General formula	Write the general rule $\det(A)=ad-bc$ for a $2\times 2$ matrix.	0:30
Practice examples	Apply the formula to more $2\times 2$ determinants.	0:55

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