Let $A,B$ be $m\times m$ matrices such that $AB$ is invertible. Show $A,B$ invertible.
106442
Show that AB is singular if A is singular
18585
Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
35757
A 2x2 matrix $M$ exists. Suppose $M^3=0$ show that (I want proof) $M^2=0$
48658
Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
128760
If $A$ and $B$ two $n\times n$ matrix such that $AB=BA$, then $\dim(A\cap B)$?
61103
Prove that $\mathbb{|Q| = |Q\times Q|}$
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
38200
Show that $(\mathbf{a}·\mathbf{a})(\mathbf{b}·\mathbf{b})-(\mathbf{a}·\mathbf{b})^2=(\mathbf{a}\times\mathbf{b})·(\mathbf{a}\times\mathbf{b})$?
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
23372
Show that for an invertible matrix, the images of a set of vectors spanning the space also form a spanning set
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
32103
Show that for a $2\times 2$ matrix $A^2=0$
124734
If $A^3=O$ is the matrice $A^2-A+I$ invertible?
52357
If $a,b \in G$, show that $ab^{n}a^{-1}=(aba^{-1})^{n}$.
123044
Commutative matrices are multiples of the identity
35834
Is the product of any two invertible diagonalizable matrices diagonalizable?