If $A$ is an $n$-by-$n$ matrix with characteristic polynomial $(-1)^nt^n+b_{n-1}t^{n-1}+\cdots+b_1t+b_0$, show that $tr(A)=(-1)^{n-1}b_{n-1}$
100899
Coefficients of the characteristic polynomial
75002
show that $\det(A)=0$ in this case
88466
Show that polynomial $X^{n+1}-aX^n+aX-1$ has only roots of module $1$
110086
Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues
81181
Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
82295
Showing that the minimal polynomial of an $n \times n$ matrix has degree at most $n$ without using the Cayley-Hamilton Theorem
125763
If $\mathrm{tr}(A)=0$, then we have $A=BC-CB?$
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
104037
Jordan normal form for a characteristic polynomial $(x-a)^5$
149086
Determining $\mbox{tr}(A)$ and $\det(A)$ as functions of the eigenvalues of a matrix
35278
Does equality of characteristic polynomials guarantee equivalence of matrices?
45658
Determinant of a special $n\times n$ matrix
103854
Showing that $Q_n=D_n+D_{n-1}$
132213
Is every real monic polynomial the characteristic polynomial of a real matrix?
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
41514
Let $trcA=0$.why $A=M+N$ where $M$ and $N$ are nilpotent matrices?
57543
Show that a matrix is nilpotent.