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BITSAT Mathematics Matrices 2024 BITSAT 2024 (Memory Based Paper 1)

BITSAT Mathematics Question (2024) — Solution

Question

If A is a square matrix of order 3 , then Adj ( Adj .A^2 ) =

Options

  1. A. |A|^2
  2. B. |A|^4
  3. C. |A|^8
  4. D. | A |^ 16

Answer

C. |A|^8

Step-by-step solution

| adj ( adj A^2 ) |= | adj A |=| A |^ n-1 =| A |^2 | adj A^2 |=| adj A|^2= (|A|^2 )^2=|A|^4 | adj ( adj A^2 ) |= (|A|^4 )^ 3-1 = (|A|^4 )^2=|A|^8

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