A is a nxn matrix with zero as an eigenvalue. Show that $A$ is not invertible.
52208
Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.
78307
Under what conditions is $AA^T$ invertible?
898
Strictly diagonally dominant matrices are non singular
5322
Let $A$ be a complex matrix such that $A^n = I$, show that $A$ is diagonalisable.
41932
Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
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 $\det(A)$?
126990
Invertible matrix and inverse matrix
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
111550
Let $A$ be a square complex matrix of size $n$ then $\langle Ax,x\rangle=0$ for $\forall x \in \Bbb C^n$ $\iff A=0$
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
90402
$AB$ is not invertible
58021
Finding matrix $B$ is not zero matrix where $AB= 0$
98646
Show determinant of matrix is non-zero
86125
If $A$ is idempotent, then the eigenvalues of $A$ are $0$ or $1$
57296
A non-diagonal $4\times4$ matrix such that $A^3=A^2=0$ and its rank is $2$
19649
A question about the proof of "a symmetric matrix has real eigenvalues".
124942
Prove that an upper triangular matrix is invertible if and only if every diagonal entry is non-zero.