To prove $adj(adjA)=A$ for a Singular matrix of order $3 \times 3$
63915
the adjugate of the adjugate
89177
$\operatorname{adj}(AB) = \operatorname{adj} B \operatorname{adj} A$
6169
If $ A^3=A$ prove that $Ker\left(A-I\right)+Im\left(A-I\right)=V$
138342
Proof of a matrix exponential identity
19280
Jordan Canonical Form determined by characteristic and minimal polynomials in dimension $3$, but not beyond
21758
Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal
78224
Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
83853
Prove that the polar decomposition of normal matrices, $A=SU$, is such that $SU=US$
131212
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
146243
Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
19203
Is the rank of a matrix the same of its transpose? If yes, how can I prove it?
115137
Product of adjacency matrices
7457
Prove that $J^+AJ$ has positive eigenvalues
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
129743
$A$ be a $2\times 2$ real matrix with trace $2$ and determinant $-3$
54740
Proofs of Determinants of Block matrices
52208
Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.