Each of the operations described here assume that the matrix algebra is defined over a commutative ring.

[Future release] Adjoint(a) : AlgMatElt -> AlgMatElt

Given an element a of a subalgebra of M_n(S), return the adjoint of a as an element of M_n(S).

Given an element a of a subalgebra of M_n(S), return the determinant of a as an element of S.

Given an element a of a subalgebra of M_n(S), return the trace of a as an element of S.

Given an element a of a subalgebra of M_n(S), return the transpose of a as an element of M_n(S).

Given an invertible matrix a over a finite field, determine the order of a.

Given an invertible matrix a over a finite field, return the order of a in factored form.

Given an invertible matrix a over a finite field, return the projective order o of a and a scalar s such that a^o = sI.

Given an invertible matrix a over a finite field, return the projective order o of a in factored form and a scalar s such that a^o = sI.