The inverse of [ cc -4 & 3 7 & -5 ] is - Vidyadip

MCQ

The inverse of $\left[\begin{array}{cc}-4 & 3 \\ 7 & -5\end{array}\right]$ is

A
$\left[\begin{array}{cc}-5 & 3 \\ 7 & -4\end{array}\right]$
B
$\left[\begin{array}{ll}5 & 3 \\ 7 & 4\end{array}\right]$
C
$\left[\begin{array}{cc}-5 & 7 \\ 3 & -4\end{array}\right]$
D
$\left[\begin{array}{ll}-5 & -3 \\ -7 & -4\end{array}\right]$

✓

Answer

Given, $A=\left[\begin{array}{cc}-4 & 3 \\ 7 & -5\end{array}\right] \therefore|A|=20-21=-1$
And adj $A=\left[\begin{array}{ll}-5 & -7 \\ -3 & -4\end{array}\right]^{\top}=\left[\begin{array}{ll}-5 & -3 \\ -7 & -4\end{array}\right]$
$
\therefore \quad A^{-1}=\frac{1}{|A|}(\operatorname{adj} A)=\left[\begin{array}{ll}
5 & 3 \\
7 & 4
\end{array}\right]
$

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