# Problem 1067

The sizes of two matrices A and B are given. Find the size of the product AB and the product BA, whenever these products exits.

A is 2 × 6, and B is 6 ×  6.

Solution:-

Find the number of rows and number of columns in A. In an m × n matrix, m represents the number of rows and n represents the number of columns.

In matrix A, the number of rows and number of columns is 6.

Find the number of rows and number of columns in B.

In matrix B, the number of rows is 6 and the number of columns is 6.

The product AB of two matrices A and B can be found only if the number of columns of A is the same as the number of rows of B.

Note that the number of columns is matrix A and the number of rows in matrix B is 6.

Thus, the product AB can be found.

The product AB will have as many rows as A and as many columns as B.

Now determine the size of the product AB. Note that A have 2 rows and B have 6 columns.

The size of the product AB is 2 × 6.

Similarly, the product BA of two matrices B and A can be found only if the number of columns of B is the same as the number of rows of A.

Note that the number of columns in B is 6 and the number of rows in A is 2, which are not the same.

Therefore, the product BA cannot be found.