The number of elements in the set where I is 2x2 identity …

Maths Matrices and Determinants JEE Main 2021 Numeric Response

Published by: CGP EDU Academic Team

Published on: August 12, 2026

The number of elements in the set

where I is 2x2 identity matrix, is :

Text Solution

Verified by Experts

The correct answer is:

(8)

(I − A) 3 = I 3 − A 3 − 3A(I − A) = I − A 3

⇒ 3A(I − A) = 0 or A 2 = A

⇒ a 2 = a, b(a + d − 1) = 0, d 2 = d

If b ≠ 0, a + d = 1 ⇒ 4 ways

If b = 0, a = 0, 1& d = 0, 1 ⇒ ways

⇒ Total 8 matrices

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