Here how can the thir option be correct because the condition is ac not equal to b2 Let M be - Physics - System of particles and rotational motion

Question

Here how can the thir option be correct because the condition is
ac not equal to b2
Let M be a 2 × 2 symmetric matrix with integer entires
Then M is invertible if

(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 non-zero entries in the main
diagonal
(D) the product of entries in the main diagonal of M is not the
square of an integer

Anuradha Sharma · Accepted Answer

Let M=abbcIf M is invertible then M≠0or ac≠b2For option A, bc'=bc≠abFor option B, ab'=ab≠bcFor option C, If b=0 , then b2=0 ⇒ ac≠0⇒neither a nor c is zero
It means M is a diagonal matrix with non zero entries in the main diagonal
For option D,Since ac≠b2 and b ∈I , then the product of main diagonal entries≠ square of an integer