Question

A and B are two non singular square matrices type 3 × 3 such that AB = A , BA = B and |A + B| ≠ 0 then
1. |A + B| = 0
2. |A + B| = 8
3. |A – B| = 1
4. |A + B| = 2

Answer 1

Correct Answer - Option 2 : |A + B| = 8

A² = (AB) A = A

B² = B

(A + B)² = 2 (A + B)

|(A + B)²| = |2(A + B)|

|A + B|² = 8 |A + B|

(A – B)² = 0