In this paper, we investigate Cartan subalgebras in the general linear algebra \(\mathfrak {gl}_{n}(\mathbb {K})\) and the special linear algebra \(\mathfrak {sl}_{n}(\mathbb {K})\) over an arbitrary field \(\mathbb {K}\) of positive characteristic \(p\) . Specifically, when \(\mathbb {K}\) is the finite field \(\mathbb {F}_{q}\) with \(q\) elements, we classify the conjugacy classes of Cartan subalgebras of \(\mathfrak {gl}_{n}(\mathbb {F}_{q})\) under the conjugation action of the general linear group \(\textrm{GL}_{n}(\mathbb {F}_{q})\) , relying solely on algebraic and combinatorial arguments. Using this elementary approach, we show that the total number of Cartan subalgebras of \(\mathfrak {gl}_{n}(\mathbb {F}_{q})\) is \(q^{n(n-1)}\) . Moreover, this result extends to the total number of Cartan subalgebras of \(\mathfrak {sl}_{n}(\mathbb {F}_{q})\) , except in the case when \(p = n = 2\) .
