I need help understanding a simple proof about determinants of matrices.

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What I don't understand:

I don't understand why in the proof

det(Q) = $λa_{i1}C_{i1}$(A) + $λa_{i2}C_{i2}$(A) + ... + $λa_{in}C_{in}$(A).

Shouldn't the det(Q) = $λa_{i1}C_{i1}$(Q) + $λa_{i2}C_{i2}$(Q) + ... + $λa_{in}C_{in}$(Q)?

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The determinant is evaluated according to the $i$th row and so the equation in the proof is correct.