Prove that an $n×n$ matrix with entries $+1$ or $-1$ has determinant divisible by $2^{n-1}$
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
84522
A better proof for $\det(P) = \pm1$ if $P$ is an orthogonal matrix
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
110200
Determinant of a Special Symmetric Matrix
51800
We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$
64742
Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
129647
$A^{-1}$ has integer entries if and only if the ${\rm det}\ (A) =\pm 1$
24873
Determinant of elementary permutation matrix
27984
Square matrices satisfying certain relations must have dimension divisible by $3$
127085
Bound on the difference of two determinants
129238
Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.
72326
Determinant of block matrix with commuting blocks
61868
Prove that $ND = DN$ where $D$ is a diagonalizable and $N$ is a nilpotent matrix.