Suppose $A^4 = 2A^2$. Show $(I-A^2) = (I-A^2)^{-1}$.
116798
First-year matrix problem: How do you show that a sum of an identity matrix and another matrix is equal to the sum's inverse?
83662
Prove that $ a $ divides $1^{a^{n}} + 2^{a^{n}} + ... + (a-1)^{a^{n}}$?
70386
Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$
118574
prove that $24 \mid a(a^2-1)$
78575
If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
43453
Is ${\sqrt2^{\sqrt2^{\sqrt2^{\sqrt2^\sqrt2}}}}^{...}=4$ correct?
62485
How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
55094
How to show $i^{-1} = -i$?
152039
Prove that $a^{2^n}=1 \mod 2^{n+2}$
52658
What are the integer solutions to $a^{b^2} = b^a$ with $a, b \ge 2$
13914
If $a^2+b^2=c^2$ then $a$ or $b$ is even.
4310
Range of $(a_{1}-a_{2})^2+(a_{2}-a_{3})^2+(a_{3}-a_{4})^2+(a_{4}-a_{1})^2$ is
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
85449
Show a,b,c congruences when $a^2+b^2=c^2$
41977
If $G$ is a group, show that $x^2ax=a^{-1}$ has a solution if and only if $a$ is a cube in $G$
118304
If $A^2 = I$ (Identity Matrix) then $A = \pm I$