I want to solve the following equation in mathematica :
DSolve[{X'[t] == A.X[t], X[0] == ( {{0},{0}} )}, X[t], t]
It is a system of 2 ODEs coupled by the matrix A, that I don't want to put in the form {{a,b},{c,d}} in order to have the output as a function of matrix exponential.
Mathematica understands that but gives a solution strangely expresed as :
{{X[t] ->
InverseFunction[Dot, 2, 2][A,
E^(t A.1)
InverseFunction[InverseFunction[Dot, 2, 2], 2, 2][A, 0]]}}
Where it indeed uses a matrix exponential, but also relies on a strange notation InverseFunction [...]
My question is how to get rid of this InverseFunction notation to have a more readable expression. Do I for example have a manner to postulate that A is a (2,2) matrix, invertible, with inverse B?
If I can hope a better result with maxima, please advise. Thanks a lot for help