Question

The element of second row and third column in the inverse of $\begin{array}{c}\left[\begin{array}{ccc}1& 2& 1\\ 2& 1& 0\\ -1& 0& 1\end{array}\right]\end{array}$ is

• A. -2
• B. -1
• C. 1
• D. 2

Answer 1

The correct option is B

-1

In $A^{-1}$, the element of $2^{nd}$ row and $3^{rd}$ column is the $c_{32}$ element of the matrix ($c_{ij}$) of co factors of element of A, (due to transposition) divided by $\Delta$ = $\begin{array}{c}\left|A\right|\end{array}$ = -2

$\therefore Requiredelement=\frac{(-1{)}^{3+2}{M}_{32}}{-2}=\frac{-(-2)}{-2}=(-1),$

$\begin{array}{c}where{M}_{32}=minorof{c}_{32}inA=\left[\begin{array}{cc}1& 1\\ 2& 0\end{array}\right]=0-2=-2.\end{array}$