Question

If $AB=I_n $ and $BA=I_m$ how would I prove that $m=n$?

score 164 · Answer 1 · 2026-04-16 07:23:11

164

Views

If $AB=I_n $ and $BA=I_m$ how would I prove that $m=n$?

Published on 16 Apr 2026 - 7:23

score 168 · Answer 2 · 2026-04-15 19:15:46

168

Views

Let $G$ be a group of order $105$. Prove that if a Sylow $3$-subgroup of G is normal then G is abelian.

Published on 15 Apr 2026 - 19:15

score 74 · Answer 3 · 2026-04-17 06:27:06

74

Views

Find $\lim_{x \to 1} \cos(\pi \cdot x) \cdot \sqrt{\frac{(x-1)^2}{(x^2-1)}} \cdot \frac{1-x}{x^2+x-1}$ (I need a review of my resolution please :) )

Published on 17 Apr 2026 - 6:27

score 108 · Answer 4 · 2026-04-17 07:14:03

108

Views

$z_n=n\left\{1-\cos\left(\frac{\theta}{n}\right)-i\sin\left(\frac{\theta}{n}\right)\right\}$ converges or diverges.

Published on 17 Apr 2026 - 7:14

score 161 · Answer 5 · 2026-04-14 02:19:49

161

Views

Improper Integrals Type 1

Published on 14 Apr 2026 - 2:19

score 54 · Answer 6 · 2026-04-15 17:24:59

54

Views

$(G,\cdot)$ is abelian $\Longleftrightarrow$ $\forall a,b \in G: (ab)^{-1}=a^{-1}b^{-1}$

Published on 15 Apr 2026 - 17:24

score 35 · Answer 7 · 2026-04-12 00:41:07

35

Views

Inductive Proof decimal representation of real numbers by taking the limit of a recursive series

Published on 12 Apr 2026 - 0:41

score 71 · Answer 8 · 2026-04-10 09:25:58

71

Views

Point spectrum of a particular operator

Published on 10 Apr 2026 - 9:25

score 76 · Answer 9 · 2026-04-17 00:30:52

76

Views

Prove that either all the elements of $G \setminus \{e \}$ are of infinite order or all the elements of $G$ are finite.

Published on 17 Apr 2026 - 0:30

score 130 · Answer 10 · 2026-04-09 11:11:06

130

Views

Continuous spectrum of operator.

Published on 09 Apr 2026 - 11:11

score 90 · Answer 11 · 2026-04-14 07:39:17

90

Views

T $\models \varphi$ iff $T \cup \{\lnot \varphi\}$ inconsistent, proof verification

Published on 14 Apr 2026 - 7:39

score 85 · Answer 12 · 2026-04-15 15:10:07

85

Views

Prove that if $P$ is a fixed point for an isometry $F$ then $P$ is also fixed for its inverse.

Published on 15 Apr 2026 - 15:10

score 150 · Answer 13 · 2026-04-16 17:09:50

150

Views

Proof checking : if $A$ and $B$ are finite sets then so $A \cap B$ finite

Published on 16 Apr 2026 - 17:09

score 180 · Answer 14 · 2026-04-13 00:33:03

180

Views

Is my proof of $|a| \leq b \iff -b \leq a \leq b$ correct?

Published on 13 Apr 2026 - 0:33

score 38 · Answer 15 · 2026-04-17 16:43:39

38

Views

Claim: $f(X)^{p^m}=f(X^{p^m})$, if $f(X)\in \Bbb Z_p[X]$ and $m\in \Bbb N$.

Published on 17 Apr 2026 - 16:43

List Question

If $AB=I_n $ and $BA=I_m$ how would I prove that $m=n$?

Let $G$ be a group of order $105$. Prove that if a Sylow $3$-subgroup of G is normal then G is abelian.

Find $\lim_{x \to 1} \cos(\pi \cdot x) \cdot \sqrt{\frac{(x-1)^2}{(x^2-1)}} \cdot \frac{1-x}{x^2+x-1}$ (I need a review of my resolution please :) )

$z_n=n\left\{1-\cos\left(\frac{\theta}{n}\right)-i\sin\left(\frac{\theta}{n}\right)\right\}$ converges or diverges.

Improper Integrals Type 1

$(G,\cdot)$ is abelian $\Longleftrightarrow$ $\forall a,b \in G: (ab)^{-1}=a^{-1}b^{-1}$

Inductive Proof decimal representation of real numbers by taking the limit of a recursive series

Point spectrum of a particular operator

Prove that either all the elements of $G \setminus \{e \}$ are of infinite order or all the elements of $G$ are finite.

Continuous spectrum of operator.

T $\models \varphi$ iff $T \cup \{\lnot \varphi\}$ inconsistent, proof verification

Prove that if $P$ is a fixed point for an isometry $F$ then $P$ is also fixed for its inverse.

Proof checking : if $A$ and $B$ are finite sets then so $A \cap B$ finite

Is my proof of $|a| \leq b \iff -b \leq a \leq b$ correct?

Claim: $f(X)^{p^m}=f(X^{p^m})$, if $f(X)\in \Bbb Z_p[X]$ and $m\in \Bbb N$.

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