Let . Then the number of invertible matrices in R is

Maths JEE - Advanced Previous Year Paper JEE-Advanced-2023-Paper-2 Numeric Response

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Text Solution

Verified by Experts

The correct answer is:

(3780)

Let us calculate when |R| = 0

Case-I ad = be = 0

Now ad = 0

Total - (When none of a & d is 0)

= 8 2 - 1 = 15 ways

Similarly be = 0 15 ways

15 x 15 = 225 ways of ad = bc = 0

Case-II ad = be 0

either a = d = b = c OR a d, b d but ad = bc

7 C 1 = 7 ways 7 C 2 x 2 x 2 = 84 ways

Total 91 ways

|R| = 0 in 225 + 91 = 316 ways

|R| O in 8 4 -316 = 3780

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