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The determinant of a 2 x 2 matrix A = \pmatrix{ a & b \cr c & d } is \det(A) = ad-bc .
The inverse of A is A^{-1} = \displaystyle \frac{1}{ad-bc} \pmatrix{ d & -b \cr -c & a }
If the determinant is zero (ie., the matrix is singular) then the matrix does not have an inverse.
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Summary/Background

The inverse of a matrix does not exist if the determinant is zero. Matrices whose determinant is not zero are called non-singular. Otherwise they are singular. To find the inverse of a 2x2 matrix:
  1. interchange the elements in the leading diagonal
  2. change the sign of the other two elements
  3. divide by the determinant

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Glossary

matrix

a rectangular or square grid of numbers.

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