Proving $\operatorname{Im}(A) = \operatorname{Ker}(A^T)^\perp$
45998
The range of $T^*$ is the orthogonal complement of $\ker(T)$
18585
Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
81040
proof about commutative operators and T-cyclic vectors
23095
Prove that T is a linear transformation
133756
Geometric interpretation of $\det(A^T) = \det(A)$
8374
How to prove that $R/I \otimes_R M \cong M / IM$
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
58741
Operator Exponential $e^A e^B = e^{A+B}$
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
138069
Proof that $\bigcap_{a\in A} \bigg(\, \bigcup_{b\in B} F_{a,b} \, \bigg) = \bigcup_{f\in ^AB} \bigg(\, \bigcap_{a \in A} F_{a,f(a)}\,\bigg) $
131212
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
89177
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$