What is the element a^23 in matrix A? A=8 -4 -3 3 -9 -5 -8 8 8

 8 -4 -3
 3 -9 -5-8  8  8

This is a matrix of 3 rows and 3 columns (it's called square matrix because the number of rows = the number of columns)
 
To localise an element of a matrix we use indices R and C, the first index being ALWAYS the row and the second, ALWAYS the column.

Hence:
A₂₃ = the element in row 2 and column 3, that is - 5

                  COLUMN
                1st   2nd   3rd
--------------------------------
          1st  | 8     -4      -3
ROW 2nd | 3     -9      -5           3rd |-8      8       8