I assume you mean how to multiply a 3x3 matrix with another 3x3 matrix.
Lets use the two matrices:
A = (a1 a12 a13; a21 a22 a23; a31 a32 a33)
i.e., the rows are (a11 a12 a13); (a21 a22 a23) and (a31 a32 a33)
B = (b11 b12 b13; b21 b22 b23; b31 b32 b33)
where the rows are (b11 b12 b13); (b21 b22 b23) and (b31 b32 b33)
The resultant matrix of product of these two 3x3 matrices will also be a 3x3 matrix, X with rows (x11 x12 x13); (x21 x22 x23) and (x31 x32 x33)
Here x11 = a11xb11 + a12xb21 + a13xb31;
x12 = a11xb12 + a12xb22 + a13xb32.........and so on
x33 = a31xb13 + a32xb23 + a33xb33.
that is how one can calculate the product of a 3x3 matrix with another 3x3 matrix.
Take the resultanta matrix as
res11 res12 res13
res21 res22 res23
res31 res32 res33
Multiplying each element of first row of 1st matrix and 1st col of 2nd matrix gives res11 value.
Follow the same for all other cell values.
Use Matrix Multiplication Tutorial at easycalculation site for more detailed explanation