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can the xperia zl play mkv files??
it seems that you need MOBO Player but I'll double check
Video Playback Decoder format Supported in file format
MPEG-4 Simple Profile Level 6,
Advanced Simple Profile Level 5
3GPP (.3gp), MP4 (.mp4)
Matroska (.mkv), AVI (.avi, .xvid),
(.mov
H.264 High Profile Level 3.2 3GPP (.3gp), MP4 (.mp4)
Matroska (.mkv), MPEG2-TS
(.ts, AAC audio)
H.263 Profile 0 Level 70 3GPP (.3gp)
Video Recording Encoder format Supported in file
http://www.sonymobile.com/global-en/products/phones/xperia-zr/specifications/#tabs
check the white paper
if it says it supports MKV then you don't need any addional app to play it
then Movie app that comes as default should support MKV automaticly and play it up 
I would really recommend getting MX Player with a seperate DTS plugin instead. In streaming a 1080P mkv over WIFI I found that MX Player outperforms the default Movie app, especially when DTS audio codec is used (the Movie app like many other movie players is unable to play the sound due to DTS codecs missing from Android).
@uliwooly : that's the whitepaper for the ZR, not the ZL.
Yes, you just need to get VLC Player from Play Store. MX Player has some problem with dts sound, but it can play the .mkv without sound.
https://play.google.com/store/apps/details?id=org.videolan.vlc.betav7neon