Question

Let \(A\) be a square matrix of order 3 whose all entries are 1 and let \(\mathrm{I}_{3}\) be the identity matrix of order 3 . Then the matrix \(A-3 I_{3}\) is
(A) invertible
(B) orthogonal
(C) non-invertible
(D) real Skew Symmetric matrix

Answer 1

Ans : (A)
Hint \(: \mathrm{A}-3 \mathrm{I}_{3}=\left[\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right],\left|\mathrm{A}-3 \mathrm{I}_{3}\right| \neq 0\)

Answer 2

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Answer 3

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