How to pretty print matrix to String in Julia?

For simple conversions usually DelimitedFiles is your best friend.

julia> a = rand(2,3);

julia> using DelimitedFiles

julia> writedlm(stdout, a)
0.7609054249392935      0.5417287267974711      0.9044189728674543
0.8042343804934786      0.8206460267786213      0.43575947315522123

If you want to capture the output use a buffer:

julia> b=IOBuffer();

julia> writedlm(b, a)

julia> s = String(take!(b))
"0.7609054249392935\t0.5417287267974711\t0.9044189728674543\n0.8042343804934786\t0.8206460267786213\t0.43575947315522123\n"

Last but not least, if you want to have a stronger control use CSV - and the pattern is the same - either use stdout or capture the output using a buffer e.g.:

julia> using CSV, Tables

julia> b=IOBuffer();

julia> CSV.write(b, Tables.table(a));

julia> s = String(take!(b))
"Column1,Column2,Column3\n0.7609054249392935,0.5417287267974711,0.9044189728674543\n0.8042343804934786,0.8206460267786213,0.43575947315522123\n"

Even more - if you want to capture the output from display - you can too!

julia> b=IOBuffer();

julia> t = TextDisplay(b);

julia> display(t,a);

julia> s = String(take!(b))
"2×3 Array{Float64,2}:\n 0.760905  0.541729  0.904419\n 0.804234  0.820646  0.435759"

What you were looking for:

b = IOBuffer()
show(b, "text/plain", rand(3, 3))
s = String(take!(b))