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If A= [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ] , then what is 23 A^3-19 A^2-4 A equal to?

Options

  1. ANull matrix of order 3
  2. BIdentity matrix of order 3
  3. C[ array lll 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 array ]
  4. D[ array lll 7 & 0 & 0 0 & 7 & 0 0 & 0 & 7 array ]

Correct answer

A. Null matrix of order 3

Step-by-step solution

Since, A= [ array lll 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 array ]=I A ^ n = I (identity matrix) Now, 23 ~A ^3-19 ~A ^2-4 ~A 23 I -19 I -4 I = O

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