alleryIf $M_{ij}$ is the minor of an element $a_{ij}$, then its cofactor $C_{ij}$ is
A$C_{ij}=M_{ij}$ for all $i,j$
B$C_{ij}=(-1)^{i-j}M_{ij}$
C$C_{ij}=(-1)^{i+j}M_{ij}$
D$C_{ij}=-(i+j)M_{ij}$
Answer & Solution
Correct answer: C. $C_{ij}=(-1)^{i+j}M_{ij}$
The cofactor of the element in the $i$th row and $j$th column is defined by $C_{ij}=(-1)^{i+j}M_{ij}$.
**Thus the sign depends on whether $i+j$ is even or odd.**
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