True or false: If $A^3 = 0$ , $A$ is not invertible. Justify answer.
73677
If the matrix $A^3 = 0$, is $A$ singular?
120407
Is every noninvertible matrix a zero divisor?
5022
Can a set containing $0$ be purely imaginary?
119156
$(a,b)=d \overset{?}{\implies} (a^3,b^3)=d^3$
121982
Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
83337
If $A ∈M_n(C)$ is such that $(Ax,x) = 0$ for all $x ∈C^n$, then $A = 0$
155272
Is a matrix with $1$s in the diagonal and off-diagonal entries with absolute value less than $1$ invertible?
158082
Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
146487
Can a non-square matrix be called "invertible"?
6169
If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$
118212
Is it true that $A^A\simeq P(A)$?
10828
If $A^2 = I$, then $A$ is diagonalizable, and is $I$ if $1$ is its only eigenvalue
144019
A strictly positive operator is invertible
52930
Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
152665
$A^TA+I$ is always invertible?
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$