Is it necessary $A^TA =I$ if $AA^T=I$ where A is a square matrix?
3301
If $AB = I$ then $BA = I$
73677
If the matrix $A^3 = 0$, is $A$ singular?
3330
Square matrices, ABA = A?
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
52928
If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
116539
Eigenvalues of matrix satisfying $A^2 = A$
12096
If $a+1/a$ is an integer, then so is $a^t+1/a^t$ for $t\in\mathbb N$
145397
How to prove that for every $i$, $a_i = i$
11857
$A$ be a complex $3\times 3$ matrix such that $A^3=-I$
87425
Prove that if $A$ is a square matrix with integer entries and $\det(A) = \pm 1$, then $A^{-1}$ contains all integer entries.
70157
Is every matrix $A$ such that $A^k=I$ diagonalizable?
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
141173
Are there matrices such that $AB=I$ and $BA \neq I$
24809
For all square matrices $A$ and $B$ of the same size, it is true that $(A+B)^2 = A^2 + 2AB + B^2$?
158082
Is $\|A^n\|=\|A\|^n$ true for any normal operator in a Hilbert space?
3150
Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
75690
Does the given matrix have a square root?