Suppose $T^{k+1}=0$. Show that $I + T + T^2 + \dots+ T^k = (I - T)^{-1}.$
22563
Units and Nilpotents
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
127169
Show that the zeros of $\sum_{k=1}^n kz^{k-1}$ are inside the unit disc
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
51706
If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$
20110
How to prove $(AB)^T=B^T A^T$
36090
$TT^*=T^2$, show that $T$ is self-adjoint
136737
Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$
118949
If $(Tx \mathbin{|} x) = 0$ for all $x$ then $T = 0$
112707
Must $Q^\mathsf{T}Q = I$ if $(Qx)^\mathsf{T}(Qx) = x^\mathsf{T}x$
136574
Show $g^{(n)}(0)=0$ for all $n$
16789
Prove that $T^2$ is the zero transformation if and only if $\mathrm{range}(T) \subseteq \ker(T)$.
75002
show that $\det(A)=0$ in this case
109674
If $(I-T)^{-1}$ exists, can it always be written in a series representation?
17390
Find $LK_1^2 + LK_2^2 + \dots + LK_{11}^2$.
52113
Proof by Induction $\sum_{i=0}^{k-1} 2^i = 2^k-1$