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Anonymous User Best Answer
A square matrix is invertible if and only if its columns are linearly independent. for the first column we get p²−1 for the first vector ( there are p² vectors with 0 vector ) for your second column, once you fix the first one you only have to make sure it is not a multiple of the first one.there are exactly p-1 linear combinations of the first vector because you have exactly p-1 scalars to multiply the first one so we get p²-1-(p-1)=p²-p Therefore the number of invertible matrices (p²-1)(p²-p) in Zp