I need help with this problem:
For every $i,j \in \{1,2,\dots,n\}$ is $d_{i,j} = \min\{i,j\}$. Calculate determinant of a matrix $[d_{i,j}]_{n_\times n}$.
Is it right that all the elements of this squared matrix are $1$, because of that $d_{i,j}=min\{i,j\}$? Then, value of determinant is $0$.
This matrix has determinant $1$, see here. The matrix looks as follows $$ \begin{pmatrix} 1 & 1 & 1 & \cdots & 1 \cr 1 & 2 & 2 & \cdots & 2 \cr 1 & 2 & 3 &\cdots & 3 \cr \vdots & \vdots & \vdots & \ddots & \vdots \cr 1 & 2 & 3 & \cdots & n \end{pmatrix} $$