JEE Advanced | 2014MatricesHard
Question
Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if
Options
A.The first column of M is the transpose of the second row of M
B.The second row of M is the transpose of the first column of M
C.M is a diagonal matrix with nonzero entries in the main diagonal
D.The product of entries in the main diagonal of M is not the square of an integer
Solution
Let M = 
, where a, b, c ∈ I
for invertible matrix, det(M) ≠ 0 ⇒ ac - b2 ≠ 0
i.e. ac ≠ b2
So, options (C) & (D) satisfies the above condition.
, where a, b, c ∈ I for invertible matrix, det(M) ≠ 0 ⇒ ac - b2 ≠ 0
i.e. ac ≠ b2
So, options (C) & (D) satisfies the above condition.
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