Let A = a i j 5 × 5 is a matrix such that a i j = 3 ∀ i = j 0 ∀ i ≠ j . If a d j ( a d j A ) 3 = 3 λ , then λ is equal to (where, a d j ( M ) represents the adjoint matrix of matrix M )

Question

Let A = a i j 5 × 5 is a matrix such that a i j = 3 ∀ i = j 0 ∀ i ≠ j . If a d j ( a d j A ) 3 = 3 λ , then λ is equal to (where, a d j ( M ) represents the adjoint matrix of matrix M ),

MARKS App · Accepted Answer

A = 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 3 = A = 3 5 a d j a d j A 3 = A 4 2 3 5 = A 16 3 5 = 3 80 3 5 = 3 75 = 3 150 ⇒ λ = 150

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