OK, first you need to populate your matrices. Matrix a is 2 x 3 which means two rows and three columns. The upper left space is numbered space 11., meaning row 1 column 1. The algorithm for figuring out what goes there is that you need to multiply the row and column numbers together. 1×1 is one. So you put a one in the upper left space. Continue to populate your matrix in that manner. You will get the first row as 1 2 2. Go ahead and figure out the second row.
Matrix B is 3 x 2, which means three rows, two columns. The algorithm for figuring out what goes in the upper left space, and all spaces, is to Subtract the column number j from the row number i. For example, the upper left space is 11 and 1-1=0 so a zero goes in the upper left space. The first column of the second matrix will be 0 1 2. You figure out the second column.
These two matrices can be multiplied since the first one is 2x3 and the second one is 3x2 and the inner numbers match. Multiplying will give you a 2x2 matrix. So, you multiply the matrices as you multiply any matrix pair. For example, for the upper left space, you multiply the first row of A times the first column of B and add all the results. That will be 1×0+2×1+2×2 which gives you a result of six. That goes in the upper left of the four spaces in matrix AB. Continue in this way until you have solved the problem.
