query: If $A^2=0$, then $I−A$ is invertible
positive_passages.docid: 22666
positive_passages.text: Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
negative_passages.docid: 77764
negative_passages.text: Is "$a + 0i$" in every way equal to just "$a$"?
negative_passages.docid: 125195
negative_passages.text: If matrix A is invertible, is it diagonalizable as well?
negative_passages.docid: 144019
negative_passages.text: A strictly positive operator is invertible
negative_passages.docid: 79276
negative_passages.text: Find $\min(\operatorname{trace}(AA^T))$ for invertible $A_{n\times n}$
negative_passages.docid: 145125
negative_passages.text: How to prove that $A^{-1} + B^{-1}$ is invertible given the conditions
negative_passages.docid: 6169
negative_passages.text: If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$
negative_passages.docid: 75215
negative_passages.text: Properties of invertible matrices
negative_passages.docid: 28861
negative_passages.text: Given an invertible matrix $A$ such that all elements in $A$ and in $𝐴^{−1}$ are integers, find $|𝐴^4|$
negative_passages.docid: 112485
negative_passages.text: Allowing the zero element in a field to have an inverse
negative_passages.docid: 69509
negative_passages.text: Showing a Linear Transformation is invertible
negative_passages.docid: 86125
negative_passages.text: If $A$ is idempotent, then the eigenvalues of $A$ are $0$ or $1$
negative_passages.docid: 78307
negative_passages.text: Under what conditions is $AA^T$ invertible?
negative_passages.docid: 14161
negative_passages.text: Proof of when is $A=X^TX$ invertible?
negative_passages.docid: 5526
negative_passages.text: Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
negative_passages.docid: 78575
negative_passages.text: If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$
negative_passages.docid: 15908
negative_passages.text: Is it true that $\int_{a}^b h^2=0\implies h=0$?