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  4. Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then the matrix A - 3I3 is

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Q. 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

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Solution:

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