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

Question

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 (A) invertible (B) orthogonal (C) non-invertible (D) real Skew Symmetric matrix

Tardigrade Admin · Accepted Answer

A - 3I3 = [0&1&1 1&0&1 1&1&0], |A - 3I3| ≠ 0

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 $A - 3 I_{3}$ is

invertible

orthogonal

non-invertible

real Skew Symmetric matrix

$A - 3 I_{3} = ⎣ ⎡ 011101110 ⎦ ⎤, ∣ A - 3 I_{3} ∣ \neq = 0$

Q. 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