Question

Let A be a square matrix of order 3 whose all entries are 1 and let $I_3$ be the identity matrix of order 3. Then the matrix $A - 3I_3$ is

• A. invertible
• B. orthogonal
• C. non-invertible
• D. real Skew Symmetric matrix

Answer 1

Answer: (A)

invertible

Answer 2

$A - 3I_{3} = \begin{bmatrix}0&1&1\\\ 1&0&1\\\ 1&1&0\end{bmatrix}, \left|A - 3I_{3}\right| \ne 0$