Chapter 2.3, Problem 1E

For each of the following, compute (i) $\det \left(A\right)$ , (ii) adjA, and (iii) $A^{-1}$ :

(a) $A=\left[\begin{array}{cc}1& 2\\ 3& -1\end{array}\right]$

(b) $A=\left[\begin{array}{cc}3& 1\\ 2& 4\end{array}\right]$

(c) $A=\left[\begin{array}{ccc}1& 3& 1\\ 2& 1& 1\\ -2& 2& -1\end{array}\right]$

(d) $A=\left[\begin{array}{ccc}1& 1& 1\\ 0& 1& 1\\ 0& 0& 1\end{array}\right]$