Inverse Matrix

[AlonsoMcLaren]

Is it always true that (see the attachment)?

[AlonsoMcLaren]

I am assuming that phi is a matrix and its elements depend on t, another variable.

[HallsofIvy]

In order for this to make sense, \phi would have to be a one-to-one function from a set of matrices onto itself. And it asks if the inverse function, appled to matrix x, is the same as the inverse of \phi(x).