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 $\endgroup$ –
linear algebra - How to prove $\det \left (e^A\right) = e . . . 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
prove that $\\det(ABC) = \\det(A) \\det(B) \\det(C)$ [for any $n×n . . . I was thinking about trying to argue because the numbers of a given matrix multiply as scalars, the determinant is the product of them all and because the order of the multiplication of det(ABC) stays the same, det(ABC) = det(A) det(B) det(C) holds true
$\\det(I+A) = 1 + tr(A) + \\det(A)$ 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
词性det. 是什么意思？ - 百度知道 (grammar 语法) (abbreviation det in this dictionary 本词典缩略为 det ) 限定词（置于名词前起限定作用，如the、some、my等） 。 与不可数或复数名词连用，用于否定句，也用于 疑问句 中的 if 或 whether 之后，或紧接某些动词如 prevent、ban、avoid 等）任何的，任一的。
linear algebra - how does $\det ( (\det A) I)= (\det A)^n . . . 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
The determinant of adjugate matrix - Mathematics Stack Exchange 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