Prove $|A.B|=|A|.|B|$ using matrix algebra
15452
Proving determinant product rule combinatorially
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
152817
Proving $\sup B=\inf A$
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
91829
Prove $(ah,bk)=(a,b)(h,k)\left(\frac{a}{(a,b)},\frac{k}{(h,k)}\right)\left(\frac{b}{(a,b)},\frac{h}{(h,k)}\right)$
20110
How to prove $(AB)^T=B^T A^T$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
44898
Help with commutative property of matrices problem
37162
Prove that matrices have equal rank.
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
36117
Prove that matrices of the form $\begin{pmatrix} x & x \\ x & x \end{pmatrix}$ are a group under matrix multiplication.
101803
A\(B∩C) = (A\B) ∪ (A\C) how to prove?
67483
Show that $|a-b|<\epsilon \Rightarrow |a|<|b|+\epsilon$
101040
Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$
31196
Prove $\binom{n}{a}\binom{n-a}{b-a} = \binom{n}{b}\binom{b}{a}$
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
58491
Proving the inverse of a matrix as a polynomial of matrices