Question:
If $C_{i j}$ is the cofactor of the element $a_{i j}$ of the matrix $A=\left[\begin{array}{ccc}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{array}\right]$, then write the value of $a_{32} C_{32}$.
Solution:
In the given matrix $A=\left[\begin{array}{ccc}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{array}\right]$,
$C_{32}=(-1)^{3+2}(8-30)=22$
Therefore, $a_{32} C_{32}=5 \times 22=110$.
Hence, the value of $a_{32} C_{32}$ is 110 .
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