Does $AA^T=I$ imply that $A^TA=I$?
3301
If $AB = I$ then $BA = I$
10828
If $A^2 = I$, then $A$ is diagonalizable, and is $I$ if $1$ is its only eigenvalue
50384
A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum
100549
If $e^A$ and $e^B$ commute, do $A$ and $B$ commute?
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
30996
If $\langle Ta, a\rangle \in \mathbb{R}$ for all $a$ then $T$ is self-adjoint
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
86034
Is it true that for algebraic sets $V,W$ we have $I(V \times W ) =I(V) + I(W)$?
60598
Matrix $A^T A$ as sum of outer products
52621
Why is $\det(A - \lambda I)$ zero?
77486
What is the value of $i^i$?
70157
Is every matrix $A$ such that $A^k=I$ diagonalizable?
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
94383
Prove that $A^TD-C^TB=I$
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$