NTA Abhyas JEE Main2020MathematicsMatricesPractice

If A = 2 2 9 4 and A 2 + a A + b Ι = O , then a + 2 b is equal to (where, Ι is an identity matrix and O is a null matrix of order 2 respectively)

Options

A27
B- 26
C24
D12

Correct answer

B. - 26

Step-by-step solution

A = 2 2 9 4 ⇒ A 2 = 2 2 9 4 2 2 9 4 = 22 12 54 34 a A = 2 a 2 a 9 a 4 a ,   b Ι = b 0 0 b A 2 + a A + b Ι = 22 + 2 a + b 12 + 2 a 9 a + 54 34 + 4 a + b = O ⇒ a = - 6 ⇒ 22 + 2 a + b = 0 ⇒ b = - 1 0 ⇒ a + 2 b = - 2 6

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