Maths-
General
Easy

Question

(adj AT) – (adj A)T equals-
 

  1. 2 |A|    
  2. 2 |A| I    
  3. zero matrix    
  4. Unit matrix    

The correct answer is: zero matrix


    we are asked to solve left parenthesis a d j space A to the power of T right parenthesis space – space left parenthesis a d j space A right parenthesis to the power of T space
    space a d j A to the power of T space space minus left parenthesis a d j A right parenthesis to the power of T space space space space space
equals ∣ A to the power of T space ∣ left parenthesis A to the power of T space right parenthesis to the power of negative 1 end exponent minus left parenthesis ∣ A ∣ A to the power of negative 1 end exponent space right parenthesis to the power of T space space
equals ∣ A ∣ to the power of T space space left parenthesis A to the power of negative 1 end exponent space right parenthesis to the power of T minus left parenthesis A to the power of negative 1 end exponent right parenthesis to the power of T space space ∣ A ∣ to the power of T space space
space equals ∣ A ∣ to the power of T space left parenthesis left parenthesis A to the power of negative 1 end exponent right parenthesis to the power of T minus left parenthesis A to the power of negative 1 end exponent right parenthesis to the power of T right parenthesis space space
space equals O
     

    Therefore the correct option is zero matrix

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