If C'$_{ji}$ is a cofactor of C$^T$, how can I explain why C'$_{ji}$=C$_{ij}$

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I am stuck with this proof. Can anybody help me out?

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The $ji$ cofactor of $C^T$ is the determinant of the matrix that arises from deleting the $j-th$ row and $i-th$ column of $C^T$, with the sign $(-1)^{i+j}$. That's the same as deleting the $j-th$ column and $i-th$ row of $C$ So it's the $ij$ co-factor of $C$, since the sign won't change.