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If A is a square matrix, then what is adj ( A ⁻¹ )-( adj A )⁻¹ equal to?

Options

  1. A2| ~A |
  2. BNull matrix
  3. CUnit matrix
  4. DNone of the above

Correct answer

B. Null matrix

Step-by-step solution

aligned & Let [A]= [ array ll a & b c & d array ] & aligned A⁻¹ & = 1 |A| (a d j . A) & = 1 (a d-b c) [ array cc d & -c -b & a array ]^T= 1 (a d-b c) [ array cc d & -b -c & a array ] aligned aligned aligned & adj (A⁻¹ )= 1 (a d-b c) [ array ll a & c b & d array ]^T= 1 (a d-b c) [ array ll a & b c & d array ]...(1) & adj A= [ array cc d & -b -c & a array ] & | adj A|=(a d-b c) & ( adj A)⁻¹= 1 a d j A , [ array ll a & c b & d array ]^T= 1 a d-b c [ array ll a & b c & d array ] . ....(2) aligned Subtracting eqn. (1) a

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