If $A$ is an invertible $3\times 3$ real matrix, then $\det A^\star = \det^2A$
128723
The determinant of adjugate matrix
81770
Determinant of an $n\times n$ complex matrix as an $2n\times 2n$ real determinant
119301
Is the following matrix invertible?
42809
How can we show that $(I-A)$ is invertible?
32103
Show that for a $2\times 2$ matrix $A^2=0$
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
107128
Let $B$ be a nilpotent $n\times n$ matrix with complex entries let $A = B-I$ then find $\det(A)$
85297
find a $3 \times 3$ matrix $A$ such that $A \neq I_3$ and $A^{197}=I_3$.
131212
Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
70092
Determine the number of possible values for $\det(A)$, given that $A$ is an $n \times n$ matrix with real entries such that $A^3 - A^2 -3A +2I=0$.
9574
How to show that $\det(AB) =\det(A) \det(B)$?
55787
Is there any matrix $2\times 2$ such that $A\neq I$ but $ A^3=I$?
64644
An $r\times r$ submatrix of independent rows and independent columns is invertible (Michael Artin's book).
144145
Symmetric $3\times 3$ Matrices - Base matrix
101313
Minimal polynomial, determinants and invertibility
123044
Commutative matrices are multiples of the identity
83853
Prove that the polar decomposition of normal matrices, $A=SU$, is such that $SU=US$