How to prove that tr(A) = tr(B) given that B is similar to A
48658
Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
13026
Prove that if AB=I_m, then rk(A)=rk(B).
152817
Proving $\sup B=\inf A$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
116389
If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute
61666
Proving $ [(\vec{a}+\vec{b})\times(\vec{b}+\vec{c})]\cdot(\vec{c}+\vec{a})=2\vec{c}\cdot(\vec{b}\times\vec{a})$
10107
Prove $A\cup (A\cap B) = A$
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
47135
Prove if a = b, then f(a) = f(b) for any function f (with natural deduction)
2315
How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?
23946
Prove the definitions of $e$ to be equivalent
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
64656
how do you prove that $A\times (B\setminus C) = (A\times B) \setminus (A\times C)$?
9574
How to show that $\det(AB) =\det(A) \det(B)$?
71040
If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?
151721
Uhlmann's Theorem: proof of $\text{tr}(A^{\dagger} B) = \langle m | A \otimes B |m\rangle $
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$