Julia
Julia provides easy way to play with Matrix, you can see the full documentation at http://docs.julialang.org/en/release-0.1-0/manual/arrays/
Below are some examples of basic operations of matrix in Julia.
Addition
julia> A = [1 3 1; 1 0 0]
2x3 Array{Int64,2}:
1 3 1
1 0 0
julia> B = [0 0 5; 7 5 0]
2x3 Array{Int64,2}:
0 0 5
7 5 0
julia> +(A,B)
2x3 Array{Int64,2}:
1 3 6
8 5 0
Scalar multiplication
julia> A = [1 8 -3; 4 -2 5]
2x3 Array{Int64,2}:
1 8 -3
4 -2 5
julia> 2.A
2x3 Array{Float64,2}:
2.0 16.0 -6.0
8.0 -4.0 10.0
Transposition
julia> A = [1 2 3; 0 -6 7]
2x3 Array{Int64,2}:
1 2 3
0 -6 7
julia> A'
3x2 Array{Int64,2}:
1 0
2 -6
3 7
Matrix multiplication
julia> A = [2 3 4; 1 0 0]
2x3 Array{Int64,2}:
2 3 4
1 0 0
julia> B = [0 1000; 1 100; 0 10]
3x2 Array{Int64,2}:
0 1000
1 100
0 10
julia> *(A,B)
2x2 Array{Int64,2}:
3 2340
0 1000