KCET 2021 Math Solved Paper

Let a symmetric matrix
M=[

a	c
c	b

]
For matrix to be invertible, determinant must not be equal to zero.
|M|=ab−c2≠0
⇒ ab≠c2
Therefore, M is a diagonal matrix with non-zero entries in the main diagonal and the product of entries in the main diagonal of M is not the square of an integer.