Question

The element in the first row and third column of the inverse of the matrix $\left[\begin{array}{ccc}1& 2& 3\\ 0& 1& 2\\ 0& 0& 1\end{array}\right]$, is

• A. $-2$
• B. $0$
• C. $1$
• D. none of these

Answer 1

Answer: (C)

$1$

$A=\left[\begin{array}{ccc}1& 2& 3\\ 0& 1& 2\\ 0& 0& 1\end{array}\right]$
Here, $|A|=1$
The cofactor of element $C_{31}=3\times 1-2\times 2=7$
The element $a_{13}$ in the adjoint matrix $=C_{31}$
So, $a_{13}=7$ in adjoint matrix
Since, $|A|=1$ , so $a_{13}=7$ will be the $a_{13}$ of inverse matrix