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If A is an orthogonal matrix of order 3 and B= [ array ccc 1 & 2 & 3 -3 & 0 & 2 2 & 5 & 0 array ] , then which of the following is/are correct? 1. | AB |= 47 2. AB = BA Select the correct answer using the code given below :

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

A. 1 only

Step-by-step solution

The determinent of a orthogonal matrix is always 1 aligned & | A |= 1 & ~B = [ array ccc 1 & 2 & 3 -3 & 0 & 2 2 & 5 & 0 array ] & | B |=-10-2(-4)+3(-15) & =-47 & | AB |=| A || B | & =( 1)(-47) & = 47 aligned

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