matrix - diagram and the minimum value

Questions
1

Let ‘A’ be the matrix of degree 5 of the matrix elements

A = Table[Sin[(n - m)^2*x], {n, 1, 6}, {m, 1, 6}]

How to draw a graph of the function?–> f[x]=detA
and determine the minimum value of this function in the range of {[Pi]/2, [Pi]}

2

Clear[x, det, g]
det = Det[Table[Sin[(n - m)^2*x], {n, 1, 6}, {m, 1, 6}]];
g[y_?NumberQ] := det /. x → y

To get the min can use NMinimize.

NMinimize[{g[x], Pi/2 <= x <= Pi}, x]

Out[201]= {-15.6808053249, {x -> 1.94853409545}}

This will plot it.

Plot[g[x], {x, Pi/2, Pi}, PlotRange -> All]
3

Thank You very much