**5.2.1 Determinant of a \(2\times 2\) matrix **

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

You should be able to

- Compute the determinant of a \(2\times 2\) matrix
- Determine when a \(2\times 2\) matrix is invertible by using the determinant
- Compute the inverse of a \(2\times 2\) matrix when it exists

Our recommendation is to:

**Test your ability by trying the diagnostic quiz**. You can reattempt it as many times as you want and can leave it part-way through.**Identify which topics need more work.**Make a note of any areas that you are unable to complete in the diagnostic quiz, or areas that you don't feel comfortable with.**Watch the tutorials for these topics,**you can find these below. Then try some practice questions from the mini quiz for that specific topic.**Re-try the diagnostic quiz.**And repeat the above steps as necessary until you can pass the diagnostic test. A pass grade is 80%.

Optionally, also see if you can **apply these skills to an economic application **or look at the **additional resources** and **advanced quizzes **at the bottom of the page,

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

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

This is the second, of a sequence of applications, explaining how matrices can be used to represent the dynamic change in a labour market, in terms of the distribution of workers across labour market states (employment, unemployment, non-participation). In particular, it is demonstrated how one can obtain the determinant and the inverse of the *transition matrix*. The discussion requires conceptual understanding of determinants and inverses.

The following quiz allows you to test your understanding of using matrices to represent dynamic change in a simplified model of a labour market with two states only, and to compute the determinant and inverse of the transition matrix.

You can find **practice quizzes on each topic **in the links above the tutorial videos, or you can take the **diagnostic quiz **as many times as you like to If you want to test yourself further, then try the **advanced quiz** linked below.