Check that the number of columns in the first matrix equals the number of rows in the second matrix
Let the first matrix be (A) with size (m times n)
Let the second matrix be (B) with size (n times p)
The product matrix (C = AB) will have size (m times p)
For each entry (c_{ij}), take row (i) of (A) and column (j) of (B)
Multiply corresponding entries in that row and column
Add the products to get (c_{ij})
Repeat for every row of (A) and every column of (B)
Write the resulting values in the product matrix
Use the formula (c_{ij} = sum_{k=1}^{n} a_{ik} b_{kj})