Given

So calculate AB.

Solution

The new matrix will contain size 2 x 4. The entry in row 1 and column 1 of the new matrix will be determined by multiplying row 1 of A with column 1 of B. It means that we here multiply corresponding to entries from the row of A and the column of B and then add the results up.  Here are a couple of the entries computed all the way out.

c₁₁ = (2)(1) + (-1)(-4) + (0)(0) = 6

c₁₃  = (2)(-1) + (-1) (1) + (0) (0) = -3

c₂₄ = (-3) (2) + (6) (0) + (1)(-2) = -8

Here's the absolute solution.

In this last illustration see that we could not have done the product BA as the number of columns of B doesn't match the number of row of A. This is significant to note that just because we can calculate AB doesn't mean that we can calculate BA. Similarly, even though we can calculate both AB and BA they may or may not be similar matrix.