You add matrices by adding their respective terms - e.g. the element in the first row and sixth column of the sum is the sum of the elements in the addends' first rows and sixth columns.
Wikipedia has a nice example of matrix addition that I linked below.
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They must have the same dimensions.
No. You can only add matrices of the same size.
Only square matrices have inverses.
The singular form of matrices is matrix.
Which one of those matrices is more comfortable to sleep on?