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By applying formulation based on time reversibility, we provide the analytic theory of resonance properties of metallic nanoslit arrays. We model lossy resonant systems in which a resonance is induced by a single quasi-bound mode (QBM). It is consistent with the Fano resonance theory of quantum interference of auto-ionizing atoms and captures the essential characteristics of dissipative resonant systems. We show that time-reversibility requirements lead to analytical solutions for the resonant transmission and the associated nonreciprocal absorption in terms of a minimal number of independent basic parameters that include partial decay probabilities of resonant pathways and the non-resonant transmission amplitude. With a clear view of interfering electromagnetic field configurations and the associated absorbing processes, the theory reveals the essential physics of resonant optical transmission. In particular, the enhanced transmission peak is given by the product of partial decay probabilities and is independent of the non-resonant light wave amplitude. In a highly asymmetric coupling regime, the excitation of the QBM leads to anti-resonant extinction of the transmission, indicating a negative role of the QBM. The parity of the QBM determines occurrence of red or blue tails in the spectral profile. Absorbance measurements yield direct determination of the partial decay probabilities by which the main features of the resonant transmission are quantitatively explained. Thus, these basic parameters can be directly established experimentally. Full numerical calculations of the transmission spectra are in complete quantitative agreement with our analytical formulation for optical transmission mediated by both slit cavity modes and plasmonic modes.