Proof that $\det(A^{-1})=\frac{1}{\det(A)}$
121767
Why $\det(A^{-1}) = 1/\det(A)$?
90496
Proving $\lim \frac{x^n-a^n}{x-a}=n\cdot a^{n-1}$
155082
If $P$ is real orthogonal matrix with $\det P = -1$, prove that $-1$ is an eigenvalue of $P$.
57771
Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.
81181
Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
14646
Prove $\det(kA)=k^n\det A$
154001
$(g\circ f)^{-1}=f^{-1}\circ g^{-1}$
64742
Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
142640
Prove determinant of a matrix $=\prod_{j<i}(a_i-a_j)$
55056
To show: $\det\left[\begin{smallmatrix} -bc & b^2+bc & c^2+bc\\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right]=(ab+bc+ca)^3$
22215
How to prove Binet theorem, namely $\det ( AB ) = \det (A ) \det ( B )$?
7205
Find the determinant of $A + I$, where $A$ is a real matrix such that $AA^{\top}=I$ and $\det A<0$.
78224
Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
105707
A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
13696
Proving $\limsup\frac 1 {a_n}=\frac 1 {\liminf a_n}$ and $\limsup a_n\cdot \limsup \frac 1 {a_n} \ge 1$
37249
Suppose $A$ is a 4x4 matrix such that $\det(A)=\frac{1}{64}$