Kitzur Shulchan Aruch Chapter 11 Paragraph 3
The Laws of Mezuzah
סעיף ג צָרִיךְ לְקָבְעָהּ בִּימִין הַנִּכְנָס. וְאִם קְבָעָהּ בַּשְּׂמֹאל, פְּסוּלָה, וְצָרִיךְ לַהֲסִירָהּ וּלְקָבְעָהּ בַיָּמִין וִיבָרֵךְ עָלֶיהָ. וְאֵין חִלּוּק בָּזֶה בֵּין אִטֵּר לְאֵינוֹ אִטֵּר
The mezuzah must be affixed on the doorpost on the right side as one enters. If it is affixed on the left, it is invalid and must be removed and affixed on the right side, with a new berachah. In this regard, there is no difference whether one is left-handed or not.
General Principles of Right-Hand Mezuzah Placement
The Torah commands us to place a mezuzah on the right doorpost as we enter a room or a gate. Even if all the dwellers in the home are left-dominant, the mezuzah is placed on what would be called the “right” for most people.
This requirement generally poses no problem when affixing the mezuzah to the main entrance of the house. However, determining the proper placement of mezuzot on interior rooms which are accessible from several entrances can be quite daunting.
Whenever possible, a rabbi should make these determinations as there are many factors that must be considered, and a mezuzah placed in error on a left doorpost is invalid. In most cases, a misplaced mezuzah must be transferred to the correct post and a new berachah recited. However, if a rabbi does not say that the present position is incorrect, but rather suggests that it is preferable halachically to move it to the other post, a new berachah is not necessary.