How to prove that $(M\mathbf {a} )\times (M\mathbf {b} )=(\det M)M^{-T}(\mathbf {a} \times \mathbf {b} )$?
8970
Proving the cross product matrix tranformation identity with an alternative solution
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
20736
Prove the relation $R$ in $N \times N$ defined by $(a,b) \simeq (c,d)$ iff $ad=bc$ is an equivalence relation.
48658
Let $A$ and $B$ be $n\times n$ matrices. Suppose $A$ is similar to $B$. Prove trace($A$) = trace($B$).
79031
Determinant of the Kronecker Product of Two Matrices
51800
We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$
80684
Counter example for $(A \times B) \cap (C \times D) = (A \cap C ) \times (B \cap D)$
101040
Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$
24585
Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
83713
If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
20921
If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \leq A \leq B$, then det $A \leq$ det $B$.
88124
$M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$
75002
show that $\det(A)=0$ in this case
102817
$A,B\in M_{n}(\mathbb{R})$ so that $A>0, B>0$, prove that $\det (A+B)>\max (\det(A), \det(B))$
109710
Bijection between $\mathbb N \times \mathbb N$ and $\mathbb N$
7712
How to prove the both identity (matrix)
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$