JEE Main202127 Aug 2021Morning ShiftMathematicsMatricesActual
If the matrix A = 0 2 K - 1 satisfies A A 3 + 3 I = 2 I , then the value of K is
Options
- A1 2
- B1
- C- 1
- D- 1 2
Correct answer
A. 1 2
Step-by-step solution
A A 3 + 3 I = 2 I A 2 = 0 2 K - 1 0 2 K - 1 = 2 K - 2 - K 2 K + 1 A 3 = 2 K - 2 - K 2 K + 1 0 - 1 K 2 = - 2 K 4 K + 2 2 K 2 + K - 2 K - 2 K - 1 A 4 = 2 K - 2 - K 2 K + 1 2 K - 2 - K 2 K + 1 = 4 K 2 + 2 K               - 4 K - 4 K - 2 - 2 K 2 - 2 K 2 - K     2 K + 4 K 2 + 1 + 4 K A 4 + 3 AI = 2 I 2 I = 4 K 2 + 2 K - 8 K - 2 - 4 K 2 - K 4 K 2 + 6 K + 1 + 3 0 2 K - 1 1 0 0 1 2 I = 4 K 2 + 2 K - 8 K - 2 - 4 K 2 - K 4 K 2 + 6 K + 1 + 3 0 2 K - 1 2 I = 4 K 2 + 2 K 6 - 8 K - 2