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Question

If A is a square matrix of order 3 then ∣ Adj open parentheses bold Adj space A squared close parentheses ∣ equals

  1. vertical line A vertical line squared
  2. vertical line A vertical line to the power of 4
  3. vertical line A vertical line to the power of 8
  4. vertical line A vertical line to the power of 16

Hint:

In this question, we have to find the∣ Adj open parentheses bold Adj space A squared close parentheses ∣ if the square matrix is order n. Using the formula, open vertical bar A d j space left parenthesis A d j space A squared right parenthesis close vertical bar equals open vertical bar A squared close vertical bar to the power of open parentheses n minus 1 close parentheses squared end exponent comma space w h e r e space i s space n space o r d e r space space o f space t h e space s q u a r e space m a t r i x. space

The correct answer is: vertical line A vertical line to the power of 8


    open vertical bar A d j space left parenthesis A d j space A squared right parenthesis close vertical bar equals open vertical bar A squared close vertical bar to the power of open parentheses n minus 1 close parentheses squared end exponent
n space rightwards arrow o r d e r space space o f space t h e space s q u a r e space m a t r i x. space
open vertical bar A d j space left parenthesis A d j space A squared right parenthesis close vertical bar equals open vertical bar A squared close vertical bar to the power of open parentheses 3 minus 1 close parentheses squared end exponent equals open vertical bar A squared close vertical bar to the power of open parentheses 2 close parentheses squared end exponent equals open vertical bar A close vertical bar to the power of 8

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