The moon is 384K km away. For the mirror to be in position every night, all night, it would have to be in geostationary orbit at 36K km away. So it would have to be about 1 tenth the width to the moon to appear the same size, so about 350 km in diamter. Now happily the moon isn't very shiny, about 12% of light gets reflected. So our mirror, to reflect the same amount of light assuming 100% reflective, would only have to be about an 8th in surface are. That still makes a mirror about 120 km across. The extremely delayed James Webb telescope has a mirror of 6.5m diameter.
That only really reaches maximum brightness when most of the sunward side of the mirror is visible. Generally it would appear in the sky as a bright ellipse (Or not at all) unless it was set to rotate.