If $A$ is non-singular, prove $|A| = \frac{1}{|A^{-1}|}$?
29568
Prove that the determinant of $ A^{-1} = \frac{1}{det(A)} $- Linear Algebra
76925
Algebraic proof that if $a>0$ then $1+a^9 \leq \frac{1}{a}+a^{10} $
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
71547
Prove $ 1+\left( 1-\frac{x}{n}\right)+...+\left(1-\frac{x}{n}\right)^{n-1}=\frac{n}{x}\left(1-\left(1-\frac{x}{n}\right)^n\right)$
60900
If $A^2=-I$, Prove that $\det{A}=1$
18914
How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
103757
how can I prove that $\frac{\arctan x}{x }< 1$?
106868
Prove that $x+\frac1{4x} ≥ 1$ for $x>0$
14221
How can we prove it? ${a}{b}≤\frac{a^p}{p}+\frac{b^q}{q}$
104424
If each eigenvalueof $A$ is either $+1$ or $-1$ $ \Rightarrow$ $A$ is similar to ${A^{ - 1}}$
33097
Proving an inequality without an integral: $\frac {1}{x+1}\leq \ln (1+x)- \ln (x) \leq \frac {1}{x}$
40524
Let $A \subseteq (0,\infty$) such that $\inf A>0$. Let $\frac{1}{A}=\{\frac{1}{a},a\in A\}$. Prove that $\sup \frac{1}{A}=\frac{1}{\inf A}$.
117680
Prove that $|e^{i\theta_1}-e^{i\theta_2}| \leq |\theta_1 - \theta_2|$
137614
$\left|\frac{x}{|x|}-\frac{y}{|y|}\right|\leq |x-y|$, for $|x|, |y|\geq 1$?
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
135747
Prove $x^{rs}-1=(x^s-1)(x^{s(r-1)}+...+x^s+1)$
3110
Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$