Question

The multiplicative inverse of matrix $\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]$

• A. $\left[\begin{array}{cc}4& -1\\ 7& 2\end{array}\right]$
• B. $\left[\begin{array}{cc}4& -1\\ -7& 2\end{array}\right]$
• C. $\left[\begin{array}{cc}4& -1\\ -7& -2\end{array}\right]$
• D. $\left[\begin{array}{cc}-4& -1\\ 7& -2\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{cc}4& -1\\ -7& 2\end{array}\right]$

Matrix$=\left[\begin{array}{cc}2& 1\\ 7& 4\end{array}\right]$

$A^{-1}=\frac{1}{|A|}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$ for $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$

$|A|=2\times 4-7\times 1$

$=8-7=1$

$A^{-1}=\frac{1}{1}\left[\begin{array}{cc}4& -1\\ -7& 2\end{array}\right]$

$\therefore$ Inverse is $\left[\begin{array}{cc}4& -1\\ -7& 2\end{array}\right]$.