Behavior of ^(::Matrix{<:Integer}, ::Integer) inconsistent with behavior of ^(::Integer, ::Integer)

[afniedermayer]

^(::Matrix{Int64}, ::Int64) is type unstable. See e.g.

fibonacci_Q = [1 1;1 0]
@code_warntype fibonacci_Q^2

which shows Union{Array{Float64,2}, Array{Int64,2}}. The reason seems to be that ^(A::Matrix{Int64}, p::Int64) returns a Matrix{Float64} if p<0.

This is inconsistent with the behavior of ^(x::Int64, p::Int64), which returns an Int64 if p>=0 or if x==1 or x==-1. Otherwise, it throws a DomainError.

[afniedermayer]

A related issue (also fixed by #23368 ) is that ^(::AbstractArray{S}, ::T) where S<:Integer, T<:Integer does not promote types the same way as ^(::S, ::T). For example, [1 1;1 0]^big(10000) returns a Matrix{Int64} (which overflows) rather than Matrix{BigInt}. This behavior is different from 2^big(10000), which returns a BigInt.

I'll adjust the title of the issue to reflect this.