What is $\det(I + A^{50})$ if $A$ has eigenvalues $1$, $-1$ and $0$?
39256
Finding $\det(I+A^{100})$ where $A\in M_3(R)$ and eigenvalues of $A$ are $\{-1,0,1\}$
2271
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
141628
How did the equation $|A- \lambda I| = 0$ came for finding Eigen values of a Matrix
149086
Determining $\mbox{tr}(A)$ and $\det(A)$ as functions of the eigenvalues of a matrix
121767
Why $\det(A^{-1}) = 1/\det(A)$?
72046
Prove all eigenvalues of $A^*A$ are non-negative
129977
Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$
81275
Eigenvalue Problem -- prove eigenvalue for $A^2 + I$
60900
If $A^2=-I$, Prove that $\det{A}=1$
46825
The identity det(A) = exp(Tr(ln(A)) for A general
101631
Determinant of a finite-dimensional matrix in terms of trace
37537
Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
122951
If the $\det(A)=0$ why does the matrix $A$ have an eigenvector?
52621
Why is $\det(A - \lambda I)$ zero?
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$