Question

Inverse of the matrix $\left[\begin{array}{cc}1& -2\\ 3& 4\end{array}\right]$ is

• A. $\frac{1}{10}\left[\begin{array}{cc}1& -2\\ 3& 4\end{array}\right]$
• B. $\frac{1}{10}\left[\begin{array}{cc}4& 2\\ -3& 1\end{array}\right]$
• C. $\left[\begin{array}{cc}4& 2\\ -3& 1\end{array}\right]$
• D. $\frac{1}{10}\left[\begin{array}{cc}4& -2\\ -3& 1\end{array}\right]$

Answer 1

Answer: (B)

$\frac{1}{10}\left[\begin{array}{cc}4& 2\\ -3& 1\end{array}\right]$

$A$ $=\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$
Inverse of $A$ $=A^{-1}=\frac{1}{ad-bc}\left|\begin{array}{cc}d& -b\\ -c& a\end{array}\right|$
$\therefore$
Inverse of
$\left|\begin{array}{cc}1& -2\\ 3& 4\end{array}\right|=$ $\frac{1}{10}\left|\begin{array}{cc}4& 2\\ -3& 1\end{array}\right|$