Question

If matrix $A=\left[\begin{array}{ccc}1& 0& -1\\ 3& 4& 5\\ 0& 6& 7\end{array}\right]$ and its inverse is denoted by $A^{-1}=\left|\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{22}& a_{23}\\ a_{31}& a_{32}& a_{33}\end{array}\right|$ then the value of $a_{23}$ is equal to :

• A. 21/20
• B. 1/5
• C. -2/5
• D. 2/5

Answer 1

Answer: (C)

Given : $A=\left[\begin{array}{ccc}1& 0& -1\\ 3& 4& 5\\ 0& 6& 7\end{array}\right]$
$\therefore |A|=1(-2)-1(18)=-20$
we know that $A^{-1}=\frac{Adj.A}{|A|}$
The element $a_{23}$ will be $\frac{A_{32}}{|A|}$, because Adj.
A is the transpose of the respective cofactors founded.
Now, $A_{32}=5-(-3)=8$
Thus $a_{23}=\frac{8}{-20}=\frac{-2}{5}$