Prove that $\det A=0$ if $I \notin \operatorname{span} \{A,A^2,\dots,A^n\}$
57771
Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.
14646
Prove $\det(kA)=k^n\det A$
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
98646
Show determinant of matrix is non-zero
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 $\det(A)$?
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
152637
Determinant of a specific circulant matrix, $A_n$
63119
Let $M=\big( \begin{smallmatrix} A & B \\ C & D \end{smallmatrix} \big)$. Prove $\det(M)=\det(A)\cdot \det(D-C·A^{-1}·B)$.
10083
Determinant of matrix times a constant.
70092
Determine the number of possible values for $\det(A)$, given that $A$ is an $n \times n$ matrix with real entries such that $A^3 - A^2 -3A +2I=0$.
84341
Can the determinant of a matrix can be made $0$?
39256
Finding $\det(I+A^{100})$ where $A\in M_3(R)$ and eigenvalues of $A$ are $\{-1,0,1\}$
133756
Geometric interpretation of $\det(A^T) = \det(A)$
106619
Determinant of matrix
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
69641
Determinant identity: $\det M \det N = \det M_{ii} \det M_{jj} - \det M_{ij}\det M_{ji}$
72046
Prove all eigenvalues of $A^*A$ are non-negative