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If have a matrix $A$ that all I know about is its size and what its determinant is? For example a $4\times4$ matrix with a determinant of $3$. How can I find the determinant of the cofactor matrix $cof(A)$.

What I have done is I created a lower triangular matrix where the product of the diagonals will give me $3$. So do I just find the cofactor matrix of the matrix I came up with and find its determinant. Would that be correct?

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  • $\begingroup$ Why did you delete, then re-ask this question? $\endgroup$ – joriki Mar 19 '16 at 23:29
  • $\begingroup$ The cofactor matrix is the transpose of the adjugate matrix, so it suffices to compute the determinant of the latter. See math.stackexchange.com/questions/92837/… for that. $\endgroup$ – darij grinberg Mar 19 '16 at 23:31
  • $\begingroup$ It is quite a standard fact that the cofactor matrix has determinant $1/\det A$. $\endgroup$ – Crostul Mar 20 '16 at 0:37

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