Show that if $M $ is orthogonal matrix, then $\det M =\pm 1$.
69980
Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
94558
Show that $\phi(mn) = \phi(m)\phi(n)\frac{d}{\phi(d)}$
9574
How to show that $\det(AB) =\det(A) \det(B)$?
69641
Determinant identity: $\det M \det N = \det M_{ii} \det M_{jj} - \det M_{ij}\det M_{ji}$
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
142980
If $\,A^k=0$ and $AB=BA$, then $\,\det(A+B)=\det B$
138342
Proof of a matrix exponential identity
1770
Matrix $M_1 = M(f', \mathcal{B}, \mathcal{B '})$ of $f$
65783
Proving: "The trace of an idempotent matrix equals the rank of the matrix"
37537
Show that $det(A)=0$ for a Matrix $A$ Such That for $X=[2,3,4]^{T}$, $AX=0$
69497
Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
135252
If $M$ is positive definite, then $\operatorname{det}{(M)}\leq \prod_i m_{ii}$
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
83853
Prove that the polar decomposition of normal matrices, $A=SU$, is such that $SU=US$
60900
If $A^2=-I$, Prove that $\det{A}=1$
10083
Determinant of matrix times a constant.
134244
Determinant of a matrix will all off-diagonal elements equal