Prove that A is invertible if $A^2 - 4A -7I = 0$.
33355
Proving that matrix in equation is invertible
78463
Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
33030
Proof that $\inf A = -\sup(-A)$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
100450
Prove that 3 is a primitive root of $7^k$ for all $k \ge 1$
121982
Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
60900
If $A^2=-I$, Prove that $\det{A}=1$
118574
prove that $24 \mid a(a^2-1)$
32108
$ a\in \Bbb Z_n$ is invertible $\,\Rightarrow\gcd (a,n) =1$
151806
Prove that $A^k = 0 $ iff $A^2 = 0$
31917
If $q$ is coprime to $a$ then $a\mid nq-1,\,$ so $q$ is invertible mod $a$
10828
If $A^2 = I$, then $A$ is diagonalizable, and is $I$ if $1$ is its only eigenvalue
55428
Inductive proof of $a_n = 3*2^{n-1} + 2(-1)^n$ if $a_n = a_{n-1} + 2*a_{n-2}, a_1 = 1, a_2 = 8$
36567
$A^{T}A$ positive definite then A is invertible?