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Matrices & Determinants: Matrix Adj Adj Equals

JEE Maths question with a full step-by-step solution.

Question

A

is a

3 \times 3

matrix and

\det A = 5

, then

\det\big(\text{Adj}(\text{Adj}\,A)\big)

equals:

5^2

5^3

5^4

correct

5^5

Solution

Step 1: Apply the iterated adjoint identity For an

n \times n

matrix,

\det\big(\text{Adj}(\text{Adj}\,A)\big) = |A|^{(n-1)^2}

. Step 2: Substitute

n = 3

(n-1)^2 = 4 \implies \det\big(\text{Adj}(\text{Adj}\,A)\big) = 5^4

Answer: (3)

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