query: Inverse of $I+BA$ is $(I+BA)^{-1} = I-B(I+AB)^{-1}A$
positive_passages.docid: 64077
positive_passages.text: $I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.
negative_passages.docid: 87289
negative_passages.text: Find the multiplicative inverses of all the elements in $\Bbb Z_{16}^\times$
negative_passages.docid: 148946
negative_passages.text: If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
negative_passages.docid: 149292
negative_passages.text: Inverse of a diagonal matrix plus a constant
negative_passages.docid: 7622
negative_passages.text: $AB-BA=I$ having no solutions
negative_passages.docid: 75480
negative_passages.text: Matrix Identity $(I-G_1G_2)^{-1}G_1=G_1(I-G_2G_1)^{-1}$?
negative_passages.docid: 125719
negative_passages.text: Multiplicative inverse of a complex number.
negative_passages.docid: 98855
negative_passages.text: Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
negative_passages.docid: 9986
negative_passages.text: Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
negative_passages.docid: 20878
negative_passages.text: If $(a,b)=1$ then prove $(a+b, ab)=1$.
negative_passages.docid: 140252
negative_passages.text: Matrices - Conditions for $AB+BA=0$
negative_passages.docid: 33542
negative_passages.text: When is $A- B = B- A$?
negative_passages.docid: 62382
negative_passages.text: I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
negative_passages.docid: 74222
negative_passages.text: If $a+b=1$ then $a^{4b^2}+b^{4a^2}\leq1$
negative_passages.docid: 64742
negative_passages.text: Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
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: 26562
negative_passages.text: Inverse of $f(x)=\sin(x)+x$