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linear algebra - Why is $\det (-A)= (-1)^n\det (A)$? - Mathematics . . . Typically we define determinants by a series of rules from which $\det(\alpha A)=\alpha^n\det(A)$ follows almost immediately Even defining determinants as the expression used in Andrea's answer gives this right away On the other hand, the arguments showing $\det(AB)=\det(A)\det(B)$ are more elaborate $\endgroup$ –
$\\det(I+A) = 1 + tr(A) + \\det(A)$ for $n=2$ and for $n gt;2$? Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers