Question

Suppose the first two columns, b₁ and b₂, of B are equal. What can you say about the columns of AB (if AB is defined)? Why? Choose the correct answer below.

A. The first two columns of AB will be equal only if the first two columns of A are equal.
B. The first two columns of AB will be equal only if the first two rows of A are equal.
C. The first two columns of AB are Ab, and Ab₂. They are equal since by and b₂ are equal.
D. Nothing can be determined about the columns of AB since the entries of A are unknown.

Answer 1

The first two columns of AB will be equal only if the first two columns of A are equal.

Step-by-step explanation:

The correct answer is A. The first two columns of AB will be equal only if the first two columns of A are equal.

When multiplying matrices, the columns of the product matrix AB are linear combinations of the columns of A. Since the first two columns of B are equal (b₁ = b₂), the first two columns of AB will also be equal.