Given the matrix $A$ such that $A^3=0$. Determine if matrix $A^2-A+I$ is invertible, and if it is, find it's inverse.
124734
If $A^3=O$ is the matrice $A^2-A+I$ invertible?
126711
What is the square matrix $A$ equal to if $A=A^2$
5322
Let $A$ be a complex matrix such that $A^n = I$, show that $A$ is diagonalisable.
44596
If $A$ is a square matrix and $A^2 = 0$ then $A=0$. Is this true? If not, provide a counter-example.
146487
Can a non-square matrix be called "invertible"?
82925
Let the matrix $A=[a_{ij}]_{n×n}$ be defined by $a_{ij}=\gcd(i,j )$. How prove that $A$ is invertible, and compute $\det(A)$?
155272
Is a matrix with $1$s in the diagonal and off-diagonal entries with absolute value less than $1$ invertible?
22004
Inverse of $y = x^3 + x $?
11857
$A$ be a complex $3\times 3$ matrix such that $A^3=-I$
50010
Is this how eigenvalues of some matrix $A$ are related to the inverse of $A$?
146243
Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
115296
Under what conditions does a matrix $A$ have a square root?
71631
About idempotent and invertible matrix
114271
Why is a matrix invertible if it can be written as the product of elementary matrices?
70157
Is every matrix $A$ such that $A^k=I$ diagonalizable?
143629
Looking for insightful explanation as to why right inverse equals left inverse for square invertible  matrices
108592
Given a matrix $A$ with a known Jordan decomposition, what is the Jordan decomposition of $A^2+A+I$?