Question

Determine whether each matrix product is defined. If so, state the dimensions of the product.

$X_{2\times 2}\cdot Y_{2\times 2}$

Short answer

The required answer is that product is defined with dimensions $2\times 2$

Step-by-step solution

Step 1- Determine the inner dimensions of both the matrices

The inner dimensions for both the provided matrices are represented by the number 2.

– Determine whether the product is defined or not

As the inner dimensions of provided matrices are the same which means that the product for the provided matrices is defined.

Step 3- Write the dimensions that defines the product

As the number 2 represents the dimension that is outer so the multiplication of number 2 by itself represents the dimension related to product that is $2\times 2$