Finding the Determinant of A: Step-by-Step Guide

[p.mather]

Homework Statement

A= 1 2 CF.A= 3 -2 ADJ.A= 3 -2
2 3 -2 1 -2 1

Next i need to find determinant of A so then i can do ADJ.A / determinant.A

Homework Equations

How do i work out the determinant, is there a specific way and procedure as i am unsure.

The Attempt at a Solution

 

[HallsofIvy]

You are saying, I believe, that
A= \begin{bmatrix}1 & 2 \\ 2 & 3\end{bmatrix}
CF.A= 3 & -2 \\ -2 & 1\end{bmatrix}
(which is -A^{-1})
and
Adj A= \begin{bmatrix}3 & -2 \\ -2 & 1\end{bmatrix}

In any case, if you are attempting to find a determinant, I am surprised that you do not know that
\left|\begin{array}{cc}a & b \\ c & d\end{array}\right|= ad- bc.