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Determinant of a 2 x 2 Matrix

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Details

For the following matrix:

a =

[

a11    a12 a21    a22

]

The determinant of a, denoted by det(a), is:

det(a) =

|

a11    a12 a21    a22

|

= a11a22 − a21a12

As indicated above, the determinant of a (2 x 2) matrix is the difference of the products of the diagonal entries and the off-diagonal entries. A (2 x 2) matrix A is singular if and only if det(A) = 0. Notice the determinant is designated by the vertical bars.