Proof: Let A and B be two n x n matrices such that their product is invertible. Prove that both A and B are invertible...
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
20878
If $(a,b)=1$ then prove $(a+b, ab)=1$.
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
7034
Prove that $A+I$ is invertible if $A$ is nilpotent
133699
Proving that there is a bijection between $A$ and $B$.
152817
Proving $\sup B=\inf A$
6398
Can the product of an $4\times 3$ matrix and a $3\times 4$ matrix be invertible?
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
112701
Prove that if matrix $A$ is nilpotent, then $I+A$ is invertible.
38945
On the proof that the product of diagonal matrices is a diagonal matrix?
74460
Matrices A+B=AB implies A commutes with B
114271
Why is a matrix invertible if it can be written as the product of elementary matrices?
77941
If A, B, C, D are non-invertible $n \times n$ matrices, is it true that their $2n \times 2n$ block matrix is non-invertible?
13026
Prove that if AB=I_m, then rk(A)=rk(B).