Suppose $A$ is a 2 x 2 matrix, prove that if $A^{3} = 0$, then $A^{2} = 0$
35757
A 2x2 matrix $M$ exists. Suppose $M^3=0$ show that (I want proof) $M^2=0$
120867
How prove this two symmetric matrices $AB=0$
87441
Proof involving matrix equation
7712
How to prove the both identity (matrix)
124734
If $A^3=O$ is the matrice $A^2-A+I$ invertible?
51800
We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
54118
Proving Eigenvalue squared is Eigenvalue of $A^2$
99600
Show that a 2x2 matrix A is symmetric positive definite if and only if A is symmetric, trace(A) > 0 and det(A) > 0
73677
If the matrix $A^3 = 0$, is $A$ singular?
80544
Need verification - Prove a Hermitian matrix $(\textbf{A}^\ast = \textbf{A})$ has only real eigenvalues
129743
$A$ be a $2\times 2$ real matrix with trace $2$ and determinant $-3$
75002
show that $\det(A)=0$ in this case
142642
$A=\begin{pmatrix}0&0&1\\ 0&1&0\\ 1&0&0\end{pmatrix}$, $X^2=A$ has no solutions
85297
find a $3 \times 3$ matrix $A$ such that $A \neq I_3$ and $A^{197}=I_3$.