How can I not change the matrix

They are all equal actually:

julia> t = [1 2; 3 4]
2×2 Matrix{Int64}:
 1  2
 3  4

julia> t1 = t
2×2 Matrix{Int64}:
 1  2
 3  4

julia> t1[1,1] = 0
0

julia> t2 = t
2×2 Matrix{Int64}:
 0  2
 3  4

julia> t == t1 == t2
true

julia> t === t1 === t2
true

julia> pointer(t), pointer(t1), pointer(t2) # identical
(Ptr{Int64} @0x00007fd213d37000, Ptr{Int64} @0x00007fd213d37000, Ptr{Int64} @0x00007fd213d37000)

The variables t, t1, and t2 point to the same data, the same memory location. So when you mutate t1 you mutate all.

If you want them to be different, such that only one is modified, you have to use copy:

julia> t = [1 2; 3 4];

julia> t1 = copy(t);

julia> t1[1,1] = 0;

julia> t2 = copy(t); # or just t if you want to avoid the copy

julia> t == t1 == t2
false

julia> pointer(t), pointer(t1), pointer(t2)
(Ptr{Int64} @0x00007fd21220e900, Ptr{Int64} @0x00007fd2142f9630, Ptr{Int64} @0x00007fd2142f9a90)