If A is a square matrix of order 3 of real entries such that |A|=2 A2 operatornameadj( A )=[2 2 0 0 2 2 k 0 2], then ( k ∈ R )

Question

If A is a square matrix of order 3 of real entries such that |A|=2 A2 operatornameadj( A )=[2 2 0 0 2 2 k 0 2], then ( k ∈ R ) (A) A 3=2 I (B) | kA |=16 (C) A 2=2 A (D) trace of A 3=6

Tardigrade Admin · Accepted Answer

Correct answer is (b) | kA |=16Correct answer is (d) trace of A 3=6

Q. If $A$ is a square matrix of order 3 of real entries such that $∣ A ∣ = 2& A^{2} adj (A) = ⎣ ⎡ 20 k 220022 ⎦ ⎤$ , then $(k \in R)$

$A^{3} = 2 I$

$∣ k A ∣ = 16$

$A^{2} = 2 A$

trace of $A^{3} = 6$

Correct answer is (b) $∣ k A ∣ = 16$ Correct answer is (d) trace of $A^{3} = 6$

Q. If A is a square matrix of order 3 of real entries such that ∣A∣=2&A2adj(A)=⎣⎡​20k​220​022​⎦⎤​, then (k∈R)

A3=2I

∣kA∣=16

A2=2A

trace of A3=6