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KCET2011MathematicsMatrices

If A= [ array rr & - & array ] , then A A^ is

Options

  1. AI
  2. BA
  3. C-A
  4. DA²

Correct answer

A. I

Step-by-step solution

Given, aligned A &= [ array rr 0 & - & array ] A^ &= [ array cc & - & array ] A A^ &= [ array rr & - & array ] [ array cc & - + & array ] &= [ array cc ² + ² & - - & ² + ² array ] + & A A^ &= [ array cc 1 & 0 0 & 1 array ]=I (unit matrix) aligned Hence, A A^ =I , which is called an orthogonal matrix.

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