The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, if the products are defined. A is 4 × 2, B is 2 × 4.

When we want to multiply two matrices, we need first to check if the number of columns of the first matrix is equal the number of rows of the second matrix. Then, the resulting matrix would have the number of rows equal the number of rows of the first matrix, and the number of columns equal the number of columns of the second matrix.

That is, if we have a matrix A with dimensions a x b and a matrix B with dimensions c x d, to calculate the product AB we must have b = c, and the resulting product would have dimensions a x d.

Finally, if A is 4 x 2 and B is 2 x 4, we would have:

AB = (4 x 2) (2 x 4)

2 = 2 -> product is possible.

Dimensions of the result: 4 x 4

BA = (2 x 4) (4 x 2)

4 = 4 -> product is possible.

Dimensions of the result: 2 x 2

MrRoyal MrRoyal · Answer 2 · 2021-11-26T10:44:48+01:00

The size of a matrix is its dimension,

The size of AB and BA are 4 x 4 and 2 x 2, respectively

The dimension of matrix A is given as 4 x 2, while the dimension of matrix B is 2 x 4

Product AB

The dimension of matrix AB is the row of matrix A by the column of matrix B.

Matrix A has 4 rows, while matrix B has 4 columns.

So, the dimension of matrix AB is 4 x 4

Product BA

The dimension of matrix BA is the row of matrix B by the column of matrix A.

Matrix B has 2 rows, while matrix A has 2 columns.

So, the dimension of matrix BA is 2 x 2

Hence, the size of AB and BA are 4 x 4 and 2 x 2, respectively