The element in the third row and second column of the inverse of the…
The element in the third row and second column of the inverse of the $\operatorname{matrix}\left[\begin{array}{ccc}3 & 2 & 6 \\ 1 & 1 & 2 \\ 2 & 2 & 5\end{array}\right]$ is
$1$
$-2$
$2$
$0$
Solution
The element of third row and second column of inverse of a matrix
$=\frac{\text { Cofactor of second row and third column of the matrix }}{\text { Determinant of the matrix }}$
$\begin{aligned}
& =\frac{-(3 \times 2-2 \times 2)}{3(1 \times 5-2 \times 2)+2(2 \times 2-1 \times 5)+6(1 \times 2-2 \times 1)} \\
& =\frac{-2}{3-2+0} \\
& =-2
\end{aligned}$