How is the determinant of a 2 by 2 matrix calculated?

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vector parallelogram for addition and subtraction — linear algebra One method of adding and subtracting vectors is to place their tails together and then supply two more sides to form a parallelogram. The vector from their tails to the opposite corner of the parallelogram is equal to the sum of the original vectors. The vector between their heads (starting from the vector being subtracted) is equal to their difference.

In linear algebra, the determinant of a $2 \times 2$ matrix is a scalar value calculated from its elements.

For a $2 \times 2$ matrix represented as:

$A = (\begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{matrix})$

The determinant is calculated using the following formula:

$det A = a_{11} a_{22} - a_{12} a_{21}$

In this calculation, you multiply the elements of the main diagonal ( $a_{11}$ and $a_{22}$ ) and subtract the product of the elements of the off-diagonal ( $a_{12}$ and $a_{21}$ ).1