When does $A^{1/2}$ exists? for $A$ a square matrix.
115296
Under what conditions does a matrix $A$ have a square root?
82097
If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?
152102
Prove that for every complex $2$x$2$ matrix $A$, there exists a matrix $X$ such that $X^3=A^2$.
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
6960
Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
125164
How to prove the existence of $b$ in $Q$ such that $a<b^2<c$ in $Q$?
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
32103
Show that for a $2\times 2$ matrix $A^2=0$
119387
If $A$ is any matrix then $A^*A$ and $AA^*$ are Hermitian with non-negative eigenvalues
3330
Square matrices, ABA = A?
116539
Eigenvalues of matrix satisfying $A^2 = A$
52324
Tight bound for $T(n) = T(n^{1/2}) + 1$
64747
If $A^m=I$ then A is Diagonalizable
113168
If $a > b$, is $a^2 > b^2$?
147014
Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$
62030
$A^2=A^*A$. Why is matrix $A$ Hermitian?
75104
Existence of some type matrix