Question

Consider the matrix $A=\left[\begin{array}{ccc}1& 4& 3\\ 7& 6& 9\\ 2& 5& 8\end{array}\right].$ Then cofactor of element $9$ in matrix $A$ is

[2 marks]

• A. $-3$
• B. $3$
• C. $5$
• D. $-5$

Answer 1

The correct option is B $3$

$A=\left[\begin{array}{ccc}1& 4& 3\\ 7& 6& 9\\ 2& 5& 8\end{array}\right]$
Cofactor of element $9$ is
$C_{23}=(-1{)}^{2+3}\left|\begin{array}{cc}1& 4\\ 2& 5\end{array}\right|$
$\Rightarrow C_{23}=(-1{)}^5(5-8)$
$\Rightarrow C_{23}=3$