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What is the inverse of the matrix A= ( array ccc & & 0 - & & 0 0 & 0 & 1 array )

Options

  1. A( array ccc & - & 0 & & 0 0 & 0 & 1 array )
  2. B( array ccc & 0 & - 0 & 1 & 0 & 0 & array )
  3. C( array ccc 1 & 0 & 0 0 & & - 0 & & array )
  4. D( array ccc & & 0 - & & 0 0 & 0 & 1 array )

Correct answer

A. ( array ccc & - & 0 & & 0 0 & 0 & 1 array )

Step-by-step solution

A= [ array ccc & & 0 - & & 0 0 & 0 & 1 array ] We know, AA ⁻¹= I . Let us take first option (a) as A⁻¹ . AA ⁻¹= [ array ccc & & 0 - & & 0 0 & 0 & 1 array ] [ array ccc & - & 0 & & 0 0 & 0 & 1 array ] gathered = [ array ccc ^2 + ^2 & - + & 0 - + & ^2 + ^2 & 0 0 & 0 & 1 array ] = [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ]= I gathered

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