Question

The inverse of $\left[\begin{array}{ccc}3& 5& 7\\ 2& -3& 1\\ 1& 1& 2\end{array}\right]$ is

• A. $\left[\begin{array}{ccc}7& 3& -26\\ 3& 1& -11\\ -5& -2& 0\end{array}\right]$
• B. $\left[\begin{array}{ccc}7& 3& -26\\ 3& 1& 11\\ -5& -2& 1\end{array}\right]$
• C. $\left[\begin{array}{ccc}3& 1& 11\\ 7& 3& -26\\ -5& 2& 1\end{array}\right]$
• D. $Noneofthese$

Answer 1

The correct option is D $Noneofthese$

Let A = $\left[\begin{array}{ccc}3& 5& 7\\ 2& -3& 1\\ 1& 1& 2\end{array}\right]$, |A|=3(-7)-5(3)+7(5)=-1
Adj(A)=$\left[\begin{array}{ccc}-7& -3& 26\\ -3& -1& 11\\ 5& 5& -19\end{array}\right]A^{-1}=\frac{Adj\left(A\right)}{|A|}{A}^{-1}is\left[\begin{array}{ccc}7& 3& -26\\ -3& -1& -11\\ -5& -5& 19\end{array}\right]$