Question

Let \( A = \begin{pmatrix} \alpha & 0 \\ 1 & 1 \end{pmatrix} \) and \( B = \begin{pmatrix} 1 & 0\\ 5 & 1 \end{pmatrix} \) be two matrices where \( \alpha \) is a real number. Then

• A. \( A^2 = B \) for some \( \alpha \)
• B. \( A^2 \ne B \) for any \( \alpha \)
• C. \( A^2 = -B \) for some \( \alpha \)
• D. \( |A^2| \ne |B| \) for any \( \alpha \)
• E. \( A = -B \) for some \( \alpha \)

Hint:

Always compute matrix multiplication explicitly before comparing.

Answer 1

The Correct Option is A