Proof: $A=B^2$ for some positive definite symmetric $B$
67686
Square root of Positive Definite Matrix
94639
Proof that the rank of a skew-symmetric matrix is at least $2$
138216
$a,b,c$ are positive real numbers such that, $a+b+c\ge abc$. Prove that $a^2+b^2+c^2\ge \sqrt{3}abc$
130327
Prove that $a^2 > b^2$ ; if $a > b \geq 0$.
156541
$a^b > b^a$ or $a^b b$ where $a,b$ are positive real numbers
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
131596
Symmetric Inequality in $\mathbb{R}$
149287
Prove that $A,B>0$ and $A_{ij}0$
87397
Show that $a^2 \bmod b = (a \bmod b)^2 \bmod b$
139685
If $A^2$ and $B^2$ are similar matrices, do $A$ and $B$ have to be similar?
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
145447
bilinear form - proof
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
7457
Prove that $J^+AJ$ has positive eigenvalues
67820
Showing that $(A_{ij})=\left(\frac1{1+x_i+x_j}\right)$ is positive semidefinite
88746
Positive definiteness of the matrix $A+B$