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If matrix A= [ array cc 2 & -2 -2 & 2 array ] and A²=p A , then the value of p is

Options

  1. A6
  2. B-4
  3. C4
  4. D8

Correct answer

C. 4

Step-by-step solution

Given A = bmatrix 2 & -2 -2 & 2 bmatrix . Calculate A² by multiplying A with itself: A² = bmatrix 2 & -2 -2 & 2 bmatrix bmatrix 2 & -2 -2 & 2 bmatrix A² = bmatrix (2)(2) + (-2)(-2) & (2)(-2) + (-2)(2) (-2)(2) + (2)(-2) & (-2)(-2) + (2)(2) bmatrix A² = bmatrix 4 + 4 & -4 - 4 -4 - 4 & 4 + 4 bmatrix = bmatrix 8 & -8 -8 & 8 bmatrix We are given A² = pA . Substituting the matrices: bmatrix 8 & -8 -8 & 8 bmatrix = p bmatrix 2 & -2 -2 & 2 bmatrix bmatrix 8 & -8 -8 & 8 bmatrix = bmatrix 2p & -2p -2p & 2p bmatrix Comparing

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