If $A^3 = A$, prove that $\operatorname{Ker}(A - I) \oplus\operatorname{ Im}(A - I) = V$
6169
If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$
75520
If $a^3 =a$ for all $a$ in a ring $R$, then $R$ is commutative.
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
3433
Proof if $a \vec v = 0$ then $a = 0$ or $\vec v = 0$
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
150885
$v \otimes v' = v' \otimes v$ implies $v = av'$
94383
Prove that $A^TD-C^TB=I$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
13899
Proof that $-v = (-1)*v$
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
7015
Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
21363
Prove the uniqueness of an inner product
37985
Show that $|x|^2 = |y|^2$ with $A$ orthogonal and $Ax = \cos (θ)x − \sin (θ)y$, $Ay = \sin (θ)x + \cos (θ) y$
5758
Prove that $I+\lambda A$,$I+\lambda B$,$I+\lambda C$ are invertible and A=B=C
9140
Show $\operatorname{Aut}(C_2 \times C_2)$ is isomorphic to $S_3=D_6$
118283
Show that if $A^{n}=I$ then $A$ is diagonalizable.
44912
Prove that $ \overline {A^\complement} = (A°)^\complement $