Prove that $\gcd(\det(A),26)=1$ if a $2x2$ matrix $A$ with entries in $Z_{26}$ is invertible
64742
Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
76680
Prove that if $\gcd(a,c)=1$ and $\gcd(b,c)=1$ then $\gcd(ab,c)=1$
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
34330
How to prove $\gcd(a^2,b^2) = (\gcd(a,b))^2$?
54740
Proofs of Determinants of Block matrices
156834
Why are there $736$ matrices $M\in \mathcal M_2(\mathbb{Z}_{26})$ for which it holds that $M=M^{-1}$?
22845
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
9574
How to show that $\det(AB) =\det(A) \det(B)$?
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
142693
$\gcd(a,b) = \gcd(a + b, \mathrm{lcm}[a,b])$
157784
Prove that if $\gcd(ab,c)=1$, then $\gcd(a,c)=1$.
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $