Question

If $A=\left[\begin{array}{cc}2& -3\\ -4& 7\end{array}\right]$, then ${2A}^{-1}=$

• A. $81-2A$
• B. $91-A$
• C. $31-2A$
• D. $A-91$

Answer 1

The correct option is B $91-A$

$A=\left[\begin{array}{cc}2& -3\\ -4& 7\end{array}\right]\left|A-\lambda I\right|=0\left|\begin{array}{cc}2-\lambda & -3\\ -4& 7-\lambda \end{array}\right|=0\left(2-\lambda \right)\left(7-\lambda \right)-12=0\left(\lambda -7\right)\left(\lambda -2\right)-12=0{\lambda }^2-9\lambda +2=0A^2-9A+2I=0A-9I+2A^{-1}=02A^{-1}=9I-02A^{-1}=9I-A$

$Hence,optionBisthecorrectanswer.$