query: Intuitve explanation for $(AB)^{-1} = B^{-1}A^{-1}$
positive_passages.docid: 141922
positive_passages.text: Reason for reversing the order when transpose and inverse of a group of matrices
negative_passages.docid: 75863
negative_passages.text: how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
negative_passages.docid: 15626
negative_passages.text: Relations of a~b iff b = ak^2
negative_passages.docid: 142980
negative_passages.text: If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
negative_passages.docid: 88349
negative_passages.text: Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
negative_passages.docid: 118981
negative_passages.text: Proving $\sqrt{ab} = \sqrt a\sqrt b$
negative_passages.docid: 111515
negative_passages.text: Proving that $-a=(-1)\cdot a$
negative_passages.docid: 24499
negative_passages.text: Finding $(a, b, c)$ with $ab-c$, $bc-a$, and $ca-b$ being powers of $2$
negative_passages.docid: 21217
negative_passages.text: $G$, group. $a,b\in G$. Show that $|a|=|a^{-1}|; |ab|=|ba|$, and $|a|=|cac^{-1}|, \forall c\in G$.
negative_passages.docid: 12217
negative_passages.text: What is so special about $\alpha=-1$ in the integral of $x^\alpha$?
negative_passages.docid: 50655
negative_passages.text: Proof of $f^{-1}(B_{1}\setminus B_{2}) = f^{-1}(B_{1})\setminus f^{-1}(B_{2})$
negative_passages.docid: 108633
negative_passages.text: Why $f^{-1}(f(A)) \not= A$
negative_passages.docid: 123275
negative_passages.text: Prove $[A,B^n] = nB^{n-1}[A,B]$
negative_passages.docid: 151930
negative_passages.text: What does it mean by $t=-1$?
negative_passages.docid: 107397
negative_passages.text: Algebraic proof for the identity $\sum_{k=0}^m(-1)^{m-k}{{n \choose {k}}}= {{n-1}\choose m}$
negative_passages.docid: 6650
negative_passages.text: Why $\sqrt{-1 \times -1} \neq \sqrt{-1}^2$?
negative_passages.docid: 108923
negative_passages.text: What is wrong with this false proof? $-1=(-1)^1=(-1)^\frac{2}{2}=((-1)^2)^\frac{1}{2}=\sqrt{(-1)^2}=\sqrt{1}=1$