JEE Advanced2026MathematicsMatricesActual
Which one of the following matrices can be obtained by performing elementary row transformations on the 3 3 identity matrix?
Options
- Abmatrix 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 bmatrix
- Bbmatrix 1 & 1 & 1 2 & 3 & 4 1 & 2 & 1 bmatrix
- Cbmatrix 1 & 1 & 1 2 & 3 & 4 2 & 5 & 8 bmatrix
- Dbmatrix 1 & 1 & 1 -1 & 1 & 2 0 & 2 & 3 bmatrix
Correct answer
B. bmatrix 1 & 1 & 1 2 & 3 & 4 1 & 2 & 1 bmatrix
Step-by-step solution
Any matrix obtained by performing elementary row transformations on the identity matrix is equivalent to the identity matrix, which means it must be non-singular (invertible). Therefore, its determinant must be non-zero. Evaluating the determinant of the matrix in option (A): vmatrix 1 & 1 & 1 1 & 1 & 1 1 & 1 & 1 vmatrix = 0 Evaluating the determinant of the matrix in option (B): vmatrix 1 & 1 & 1 2 & 3 & 4 1 & 2 & 1 vmatrix = 1(3 - 8) - 1(2 - 4) + 1(4 - 3) = -5 + 2 + 1 = -2 0 Evaluating the determinant of the matr