A is a 2x2 matrix, a12=a21=0, a11 does not equal 0, a22 does not equal 0.
Show that A is regular and find inverse of A
Hi NewtoMath,
To find the inverse of a (2x2) matrix, interchange the elements in the leading diagonal, change the signs of the elements in the other diagonal and divide by the determinant of the matrix.
We have $\displaystyle A = \left( \begin{array}{cc} a_{11} & 0 \\ 0 & a_{22} \end{array} \right)$
$\displaystyle A^{-1} = \frac{1}{det A} \left( \begin{array}{cc} a_{22} & 0 \\ 0 & a_{11} \end{array} \right)$
$\displaystyle det A = \frac{1}{a{11}a_{22}}$
So, $\displaystyle A^{-1} = \left( \begin{array}{cc} \frac{1}{a_{11}} & 0 \\ 0 & \frac{1}{a_{22}} \end{array} \right)$
clearly $\displaystyle AA^{-1} = I$ I tried to find out what a regular matrix was. There are various definitions to do with stochastic matrices. The most suitable was that a regular matrix is one for which AB = BA, which is true in this case.