given the matrices a and b that we see here we are going to find the matrix a by B That is to say the multiplication of both of them to begin we must see if the product is possible and for this we must determine the order of each of the matrices the first matrix is going to be of order 2 by 3 because it has two rows and three columns the second matrix is going to be of order 3 * 2 because it has three rows and two columns for the product of matrices to be possible in this case we want to find the matrix a by B it must be fulfilled Then the number of columns of the first matrix is equal to the number of rows of the second matrix we see then that this is being fulfilled they are equal therefore we can proceed with the product of the matrices the matrix a B is going to be a matrix then of order 2 * 2 that is to say these two little numbers are the ones that are going to determine the order of the product matrix then it is going to be a matrix of two rows by two columns then let's configure it as a table that allows us to facilitate the calculation of its cells Then we are going to place the matrix a here it is going to be a 2 by two matrix then we design a little table that has two rows and two columns and we are going to address it, I'm going to put the address of each of its cells. This cell here is going to be cell 11 because it is in row one, column one. This cell here is going to be cell 12 which is in row one, column two. This is going to be cell 21 which is in row two, column one and this is going to be cell 22 because it is in row two and column two. We are going to find the element that goes in cell 11. For this, we take row 1 of matrix A and we are going to multiply its elements by those in column 1 of matrix B. In other words, we are going to take these three elements from here, row one of matrix A by the elements in column one of matrix B. We are going to do it respectively, that is, first with first, second with second, and third with third. So it would be the operation 1 * 3 + 2 * 2 + -3 by -1. So there it is, then, the multiplication of the elements, we develop those operations. 1 * 3 would give 3, 2 * 2 would give. 4 positive and -3 * would give 3 positive Then we have + 3 we perform this addition 3 + 4 would be 7 7 + 3 gives us 10 and that means then that in cell 11 we have the element 10 then now we go with cell 1 2 for that we are going to take row a row a of matrix a by column 2 of matrix B Then the elements of row 1 are going to be kept they are going to be 1 2 - 3 but now we are going to work with column two of matrix B That is 1 4 5 then we would change the second components here, that is those of column two of matrix B which would then be 1 4 and 5 then here 1 4 and 5 we perform the operations 1 * 1 is 1 + 2 * 4 is 8 and here -3 * 5 gives -15 we perform this operation 1 + 8 9 9 - 15 would give -6 so here we write -6 which is the element that goes in cell 1 2 below let's find the element that goes here in cell 2 1 then we work with row 2 of matrix a That is, the first matrix and column 1 of matrix B That is, the second then we write down the elements here let's see row 2 would be 40 - 2 and column 1 of matrix B would be 3 2 - 1 So it would be 4 * 3 plus 0 * 2 + -2 * -1 we do them we do the products respectively first with first second with second third with third 4 * 3 gives us 12 0 * 2 would give 0 and -2 * -1 would give 2 this sum then gives us 14 and 14 is the element that goes here in cell 2 1 finally we are going to find the element that goes here in cell 2 2 for this we use row 2 of matrix a and column do of matrix B let's look at row two of matrix a the elements are 4 0 - 2 4 0 - 2 those are going to stay the same the ones that are going to change are the second components because now they are those of column two of matrix B That is to say these that we have here 1 4 and 5 we solve 4 * 1 4 + 0 * 4 0 and -2 * 5 would give - 10 we solve that operation 4 - 10 would give -6 And that is the element that we wrote down here we have finished then finding the elements then to give the answer we simply undo the table and the matrix then it will be like this its elements are 10 -6 14 and -6 it is a matrix of order 2 * 2 And this is Then the result of the multiplication of matrix a by matrix B