Prove that if matrix $B$ is nilpotent, then the determinant is zero.
130268
How to prove that a nilpotent matrix is not invertible?
144082
Every $n\times n$ matrix is the sum of a diagonalizable matrix and a nilpotent matrix.
130498
Linear algebra proof regarding matrices
4998
Question on determinants of matrices changing between integer matrices
145876
$AB-BA=A$ implies $A$ is singular and $A$ is nilpotent.
122580
If N is elementary nilpotent matrix, show that N Transpose is similar to N
84341
Can the determinant of a matrix can be made $0$?
41514
Let $trcA=0$.why $A=M+N$ where $M$ and $N$ are nilpotent matrices?
259
Proving the determinant of a tridiagonal matrix with $-1, 2, -1$ on diagonal.
142640
Prove determinant of a matrix $=\prod_{j<i}(a_i-a_j)$
122951
If the $\det(A)=0$ why does the matrix $A$ have an eigenvector?
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
2798
A and B are nxn matrices, $A =B^TB$. Prove that if rank(B)=n, A is pos def, and if rank(B)<b, A is pos semi-def.
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
106322
Let $A$ and $B$ be square matrices of the same size such that $AB = BA$ and $A$ is nilpotent. Show that $AB$ is nilpotent.
37867
If $0$ is the only eigenvalue of a linear operator, is the operator nilpotent
34908
$A$ is normal and nilpotent, show $A=0$