JEE Advanced 2026 · Paper 1 · Mathematics Q3

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MathematicsSingle correct+3 / -1Question 3 of 48

Which one of the following matrices can be obtained by performing elementary row transformations on the $3\times3$ identity matrix ?

\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}

\begin{bmatrix}1&1&1\\2&3&4\\1&2&1\end{bmatrix}

\begin{bmatrix}1&1&1\\2&3&4\\2&5&8\end{bmatrix}

\begin{bmatrix}1&1&1\\-1&1&2\\0&2&3\end{bmatrix}

Answer and worked solution

Official answer: B

Each elementary row operation multiplies the determinant by a non-zero number, so any matrix obtained from $I$ this way is invertible (and every invertible matrix can be reached). Check the determinants:

(A) all rows equal: $\det=0$ .
(B) $1(3-8)-1(2-4)+1(4-3)=-5+2+1=-2\ne0$ .
(C) $1(24-20)-1(16-8)+1(10-6)=4-8+4=0$ .
(D) $1(3-4)-1(-3-0)+1(-2-0)=-1+3-2=0$ .

Only (B) is invertible.

Topics:Determinants and properties Adjoint and inverse

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JEE Advanced 2026 · Paper 1, Mathematics question 3