Please let me know how to check for the locations of nodata cells in raster images in ArcMap. The raster images has no attribute table.
Yes, you can usually see NoData cells without Spatial Analyst, directly from the raster.
On the Symbology tab, look for the Display NoData As drop down button. This is usually set to no fill/no color. You can change this to a strong color (and perhaps change other symbology for the raster to grays). The no data cells should be easy to spot. Of course, if your no data cells are distributed in tiny clusters around your raster, they may not show well and you would need to use Spatial Analyst to find them.