Question

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

• A. \[ \begin{bmatrix} 1&1&1 1&1&1 1&1&1 \end{bmatrix} \]
• B. \[ \begin{bmatrix} 1&1&1 2&3&4 1&2&1 \end{bmatrix} \]
• C. \[ \begin{bmatrix} 1&1&1 2&3&4 2&5&8 \end{bmatrix} \]
• D. \[ \begin{bmatrix} 1&1&1 -1&1&2 0&2&3 \end{bmatrix} \]

Hint:

Matrices obtained from elementary row operations on identity matrix are always: \[ \mathrm{Invertible} \] Hence: \[ \det(A)\neq0 \]

Answer 1

The Correct Option is B