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If A(t)= [ array cc t & t - t & t array ] then the product of A(t) and A(-t) is

Options

  1. AA^2(-t)
  2. BIdentity matrix
  3. CA^2(t)
  4. DNull matrix

Correct answer

B. Identity matrix

Step-by-step solution

Given A(t) = bmatrix t & t - t & t bmatrix . Then A(-t) = bmatrix (-t) & (-t) - (-t) & (-t) bmatrix = bmatrix t & - t t & t bmatrix . The product A(t)A(-t) is calculated as: bmatrix t & t - t & t bmatrix bmatrix t & - t t & t bmatrix = bmatrix ^2 t + ^2 t & - t t + t t - t t + t t & ^2 t + ^2 t bmatrix . Using the trigonometric identity ^2 t + ^2 t = 1 , we get: bmatrix 1 & 0 0 & 1 bmatrix = I . Thus, the product is the identity matrix. Answer: Identity matrix

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