Question

Let \( A = \begin{bmatrix} 0 & \alpha \\ 0 & 0 \end{bmatrix} \) and \( (A + I)^5 - 50A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \). Find \( abc + abd + bcd + acd \):

• A. 0
• B. 1
• C. -1
• D. None of these

Hint:

When solving matrix problems, use matrix operations and properties to simplify the calculations.

Answer 1

The Correct Option is A

Step 1: Apply matrix operations.
Perform matrix operations on \( A \) and \( I \), and then compute the required determinant expression. After simplification, the value is 0.
Thus, the correct answer is (1).