We present analytic expressions for three-flavor neutrino oscillations in presence of invisible neutrino decay and matter effects. Using the well-known Cayley-Hamilton formalism, the leading-order terms are derived for oscillation probabilities in all major channels assuming the neutrino mass eigenstate ν3 to decay. Our work extends and complements previous studies utilizing the Cayley-Hamilton theorem, providing the series expansions for νe→νe, νe→νμ, νe→ντ, νμ→νμ, and νμ→ντ. The accuracy of the analytical formulas is investigated by comparing the results with numerically calculated probabilities. We also comment on the implications on unitarity violation.