Chapter 2.1, Problem 2E

Use determinants to determine whether the following $2\times 2$ matrices are nonsingular:

(a) $\left[\begin{array}{cc}3& 5\\ 2& 4\end{array}\right]$

(b) $\left[\begin{array}{cc}3& 6\\ 2& 4\end{array}\right]$

(c) $\left[\begin{array}{cc}3& -6\\ 2& 4\end{array}\right]$