If $ \det\left(A+X\right)=\det\left(B+X\right) $ for any $ X $ then $ A=B $
106305
Prove/disprove: if $\det(A+X) = \det(B + X)$ for all $X$, then $A=B$
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
60900
If $A^2=-I$, Prove that $\det{A}=1$
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
101803
A\(B∩C) = (A\B) ∪ (A\C) how to prove?
101040
Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$
145397
How to prove that for every $i$, $a_i = i$
109318
Equivalence relation $(a,b) R (c,d) \Leftrightarrow a + d = b + c$
78224
Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
18714
$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
22215
How to prove Binet theorem, namely $\det ( AB ) = \det (A ) \det ( B )$?
25713
If $a$ and $b$ commute and $\text{gcd}\left(\text{ord}(a),\text{ord}(b)\right)=1$, then $\text{ord}(ab)=\text{ord}(a)\text{ord}(b)$.
49109
Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
32487
Proving $\det \left( \begin{smallmatrix} A & -B \\ B & A \end{smallmatrix} \right) =|\det(A+iB)|^2$