Proof matrix $A=\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}^n , \text{ when } n \in \mathbb{N}$
37252
How can I show that $\begin{pmatrix} 1 & 1 \\ 0 & 1\end{pmatrix}^n = \begin{pmatrix} 1 & n \\ 0 & 1\end{pmatrix}$?
33448
Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
38635
How to prove that the matrix $A^k$ approaches $0$ as $k$ approaches infinity
127127
Prove condition number of a invertible matrix is atleast one
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
73155
Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
138342
Proof of a matrix exponential identity
46780
Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
115582
Prove that if a product$ AB$ of $n\times n$ matrices is invertible, so are the factors $A$ and $B$.
41813
How to prove positive (semi-)definitness in matrix notation without numbers
89175
Proof of $(a+b)^{n+1}$
54740
Proofs of Determinants of Block matrices
42435
Proof of this result related to Fibonacci numbers: $\begin{pmatrix}1&1\\1&0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&F_n\\F_n&F_{n-1}\end{pmatrix}$?
32155
Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$