Question

In which of the following situation(s) can you say that A×B=B×A?

a) A is the additive identity.
b) A and B are matrices.
c) A and B are real numbers.
d) A is the multiplicative identity.

Answer 1

You can say A×B = B×A when A and B are real numbers (c), and when A is the multiplicative identity (d). However, this does not hold true when A is the additive identity (a) or when A and B are matrices (b), except under specific circumstances where matrix A and matrix B happen to commute.

Step-by-step explanation:

In mathematics, specifically when dealing with multiplication, we encounter the property that A×B = B×A. This statement is true in certain cases:

• (c) A and B are real numbers: For real numbers, the commutative property holds for multiplication, meaning that A×B will indeed equal B×A.
• (d) A is the multiplicative identity: The multiplicative identity is 1, and for any number B, 1×B = B×1, so this is also correct.

However, for:

• (a) A is the additive identity: The additive identity does not apply to multiplication, so this situation does not make A×B = B×A true.
• (b) A and B are matrices: For matrices, multiplication is not commutative in general. This means that A×B does not necessarily equal B×A.