the sizes of matrices a and b are given. find the sizes of ab and ba whenever they are defined. (if the matrix product is undefined, enter undefined.)
a is of size 6 × 7, and b is of size 7 × 6.
ab
ba

 The required answers are

AB is of order  6 × 6.

BA is of order  7  × 7.

Step-by-step explanation:  Given that the sizes of the matrices A and B are as follows :

A is of size 6 × 7   and   B is of size 7 × 6.

We are to find the sizes of AB and BA whenever they are defined.

We know that

if a matrix P has m rows and n columns, then its size is written as m × n.

Also, two matrices P and Q of sizes m × n and r × s respectively can be multiplies if the number of columns in P is equal to the number of rows in Q.

That is, if n = r. And the size of the matrix P × Q is m × s.

Now, since the number of columns in A is equal to the number of rows in B, the product A × B is possible and is of order 6 × 6.

Similarly, the number of columns in B is equal to the number of rows in A, the product B × A is possible and is of order 7 × 7.

Thus, the required answers are

AB is of order  6 × 6.

BA is of order  7  × 7.

ok

step-by-step explanation:

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