question 3

Essay

$$\text { Prove or disprove that } \boldsymbol { A } \boldsymbol { B } = \boldsymbol { B } \boldsymbol { A } \text { whenever } \boldsymbol { A } \text { and } \boldsymbol { B } \text { are } 2 \times 2 \text { matrices. }$$

---

Definitions:

Defined Benefit Pension Plan

A type of pension plan where an employer promises a specified pension payment upon retirement, determined by an employee's earnings history, tenure of service, and age.

Interest Cost Component

The portion of pension expense that reflects the increase in the projected benefit obligation due to the passage of time.

Defined Benefit Pension Plan

A defined benefit pension plan is a retirement plan where the employer promises a specified pension payment upon retirement, based on an employee's earnings history, tenure of service, and age.

Projected Benefit Obligation

An estimation of the present value of a retirement plan's liabilities owed to employees, based on projected salary increases.