Question

If \( A^2 = 4A + 3I \) and \( A^{-1} = xA + yI \), then the value of \( (x + y) \) is :

• A. \( -1 \)
• B. \( 1 \)
• C. \( \frac{5}{3} \)
• D. \( 7 \)

Hint:

Instead of computing complex characteristic polynomials, simply isolate \( I \) in the polynomial equation: \( 3I = A^2 - 4A \). Multiplying by \( A^{-1} \) directly gives \( 3A^{-1} = A - 4I \).

Answer 1

The Correct Option is A