It is not clear from your post what exactly the structure of the matrix is. The worst case scenario is a dense symbolic 13 by 13 matrix, that is a matrix with none (or nearly none) of its entries equals to zero and which entries are not numbers but symbols (such as a, b, or c) or, worst, symbolic expressions (such as sin(alpha) or cos(theta)).
So why this is bad?
Because, the determinant of such a matrix is a polynomial made of 13! terms, that is this polynomial has more than six billions of terms (6,227,020,800 exactly). Moreover, each individual term is a product of 13 variables. Combinning both numbers (and assuming the unrealistic assumption that any symbol does occupy only one byte in memory), you would need about 80 GB (~80 billions of bytes) of memory to hold the determinant.
Therefore, it seems perfectly reasonable that Maple complains about the lack of enough available memory.
If you can reduce the size of the matrix, say just for experimental purpose, you should be able to compute a 10x10 or even a 11x11 determinant. What you can do with the output is another story.
The examples below are just to illustrate the patterns when computing a 2x2, 3x3, and 4x4 determinants.

> with(LinearAlgebra);
> Determinant(Matrix(2, 2, {(1, 1) = n[1, 1], (1, 2) = n[1, 2], (2, 1) = n[2, 1], (2, 2) = n[2, 2]}));
n[1, 1] n[2, 2] - n[1, 2] n[2, 1]
> Determinant(Matrix(3, 3, {(1, 1) = n[1, 1], (1, 2) = n[1, 2], (1, 3) = n[1, 3], (2, 1) = n[2, 1], (2, 2) = n[2, 2], (2, 3) = n[2, 3], (3, 1) = n[3, 1], (3, 2) = n[3, 2], (3, 3) = n[3, 3]}));
n[1, 1] n[2, 2] n[3, 3] - n[1, 1] n[2, 3] n[3, 2] + n[2, 1] n[3, 2] n[1, 3]
- n[2, 1] n[1, 2] n[3, 3] + n[3, 1] n[1, 2] n[2, 3]
- n[3, 1] n[2, 2] n[1, 3]
> Determinant(Matrix(4, 4, {(1, 1) = n[1, 1], (1, 2) = n[1, 2], (1, 3) = n[1, 3], (1, 4) = n[1, 4], (2, 1) = n[2, 1], (2, 2) = n[2, 2], (2, 3) = n[2, 3], (2, 4) = n[2, 4], (3, 1) = n[3, 1], (3, 2) = n[3, 2], (3, 3) = n[3, 3], (3, 4) = n[3, 4], (4, 1) = n[4, 1], (4, 2) = n[4, 2], (4, 3) = n[4, 3], (4, 4) = n[4, 4]}));
n[1, 1] n[2, 2] n[3, 3] n[4, 4] - n[1, 1] n[2, 2] n[3, 4] n[4, 3]
+ n[1, 1] n[3, 2] n[4, 3] n[2, 4] - n[1, 1] n[3, 2] n[2, 3] n[4, 4]
+ n[1, 1] n[4, 2] n[2, 3] n[3, 4] - n[1, 1] n[4, 2] n[3, 3] n[2, 4]
- n[2, 1] n[1, 2] n[3, 3] n[4, 4] + n[2, 1] n[1, 2] n[3, 4] n[4, 3]
- n[2, 1] n[3, 2] n[4, 3] n[1, 4] + n[2, 1] n[3, 2] n[1, 3] n[4, 4]
- n[2, 1] n[4, 2] n[1, 3] n[3, 4] + n[2, 1] n[4, 2] n[3, 3] n[1, 4]
+ n[3, 1] n[1, 2] n[2, 3] n[4, 4] - n[3, 1] n[1, 2] n[4, 3] n[2, 4]
+ n[3, 1] n[2, 2] n[4, 3] n[1, 4] - n[3, 1] n[2, 2] n[1, 3] n[4, 4]
+ n[3, 1] n[4, 2] n[1, 3] n[2, 4] - n[3, 1] n[4, 2] n[2, 3] n[1, 4]
- n[4, 1] n[1, 2] n[2, 3] n[3, 4] + n[4, 1] n[1, 2] n[3, 3] n[2, 4]
- n[4, 1] n[2, 2] n[3, 3] n[1, 4] + n[4, 1] n[2, 2] n[1, 3] n[3, 4]
- n[4, 1] n[3, 2] n[1, 3] n[2, 4] + n[4, 1] n[3, 2] n[2, 3] n[1, 4]

Regards,
--
Jean-Marc