Question

If matrix $A = \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix}$ and $A^2 = kA$, then the value of $k$ is:

• A. 1
• B. -2
• C. 2
• D. -1

Hint:

Always multiply carefully and match the matrix form.

Answer 1

The Correct Option is C

Compute $A^2$: \[ A^2 = A \cdot A = \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix} = \begin{bmatrix} (1)(1)+(-1)(-1) & (1)(-1)+(-1)(1) \\ (-1)(1)+(1)(-1) & (-1)(-1)+(1)(1) \end{bmatrix} = \begin{bmatrix} 2 & -2 \\ -2 & 2 \end{bmatrix}. \] So, \[ A^2 = 2A \implies k = 2. \]