Show that $A^2=A$ suppose that A is normal and $A^5=A^4$
134306
If $A$ is a normal matrix such that $A^{247} = A^{246}$, how to prove that $A$ is an orthogonal projection?
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
78575
If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$
104037
Jordan normal form for a characteristic polynomial $(x-a)^5$
41300
Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$
72313
Show that for all real numbers $a$ and $b$, $\,\, ab \le (1/2)(a^2+b^2)$
118981
Proving $\sqrt{ab} = \sqrt a\sqrt b$
29462
Suggestions on how to prove the following equality. $a^{m+n}=a^m a^n$
127293
Prove that $(a-b) \mid (a^n-b^n)$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
50410
If $A=\pmatrix{1 &0\\-1&1}$, show that $A^2-2A+I_2=0$. Hence find $A^{50}$
102234
Show $a^p \equiv a \mod 2p$
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
90486
If $(A-B)^2=O_2$ then $\det(A^2 - B^2)=(\det(A) - \det(B))^2$
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
118574
prove that $24 \mid a(a^2-1)$