Let $A$ be a $3$X$3$ matrix whose eigenvalues are $1$, $2$, $3$. Find $\det(B)$ where $B = A^2 + A^T$.
7376
Find $\det(A^{2}+A^{T})$ when eigenvalues are $1,2,3$
87425
Prove that if $A$ is a square matrix with integer entries and $\det(A) = \pm 1$, then $A^{-1}$ contains all integer entries.
125348
Does $\det(A + B) = \det(A) + \det(B)$ hold?
16439
What are the eigenvalues of matrix that have all elements equal 1?
146243
Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
72326
Determinant of block matrix with commuting blocks
70092
Determine the number of possible values for $\det(A)$, given that $A$ is an $n \times n$ matrix with real entries such that $A^3 - A^2 -3A +2I=0$.
85297
find a $3 \times 3$ matrix $A$ such that $A \neq I_3$ and $A^{197}=I_3$.
153961
Determinant of $2 \times 2$ block matrix with commuting blocks
60598
Matrix $A^T A$ as sum of outer products
110086
Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues
121800
Find the determinant of $N \times N$ matrix
1398
Find eigen values of $B = \begin{bmatrix} 0 & A^* \\ A &0 \end{bmatrix}$
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
50384
A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum
151088
Finding Matrix A from Eigenvalues and Eigenvectors (Diagonalization)
60534
What is the best algorithm to find a determinant of a matrix?