Let M be a 2 × 2 symmetric matrix with integer entries. The…

Maths Matrices and Determinants JEE (Advanced) / IIT - JEE Problems ( Previous Year ) More Than One Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if

the first column of M is the transpose of the second row of M

the second row of M is the transpose of first column of M

M is a diagonal matrix with nonzero entries in the main diagonal

the product of entries in the main diagonal of M is not the square of an integer

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(c,d)

Sol. M =

& [b c] are transpose.

So = is given ⇒ a = b = c

M = ⇒ | M | = 0 A is wrong.

[b c] & are transpose.

So a = b = c B is wrong

M = ⇒ | M | = ac ≠ 0 C is correct

M = given ac ≠ λ 2 . D is correct

(C, D) are correct.

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