JEE Advanced · 2026 · 17 May 2026 · Paper 1 · Matrices

A matrix can be obtained from the $3\times 3$ identity matrix by elementary row transformations if and only if it is non-singular (i.e., its determinant is non-zero).

Checking determinants:

• Option (A): $\left|\begin{array}{lll}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right|=0$ (all rows identical)
• Option (B): $\left|\begin{array}{lll}1& 1& 1\\ 2& 3& 4\\ 1& 2& 1\end{array}\right|=1(3-8)-1(2-4)+1(4-3)=-5+2+1=-2\ne 0$
• Option (C): $\left|\begin{array}{lll}1& 1& 1\\ 2& 3& 4\\ 2& 5& 8\end{array}\right|=0$ (row 3 = row 2 + row 1)
• Option (D): $\left|\begin{array}{ccc}1& 1& 1\\ -1& 1& 2\\ 0& 2& 3\end{array}\right|=0$

Only option (B) has non-zero determinant.