Question

Find the inverse of the given matrix: \[ A = \begin{bmatrix} 1 & 0 & 1 \\ -1 & 1 & 1 \\ 0 & 1 & 0 \end{bmatrix} \]

• A. $\dfrac{1}{2} \begin{bmatrix} 0 & 1 & 0 \\ -1 & 1 & 1 \\ 1 & 0 & 1 \end{bmatrix}$
• B. $-\dfrac{1}{2} \begin{bmatrix} 1 & 0 & 2 \\ 1 & -1 & 0 \\ 1 & 1 & -1 \end{bmatrix}$
• C. $\dfrac{1}{2} \begin{bmatrix} 1 & -1 & 1 \\ 0 & 0 & 2 \\ 1 & 1 & -1 \end{bmatrix}$
• D. $-\dfrac{1}{2} \begin{bmatrix} 0 & 1 & 0 \\ -1 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$

Hint:

For $3 \times 3$ matrices, always check determinant first. If it is zero, inverse does not exist.

Answer 1

The Correct Option is B