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GUJCET · Maths · Matrices

If \( A=\left[\begin{array}{rrr}0 & 0 & -5 \\ 0 & -5 & 0 \\ -5 & 0 & 0\end{array}\right]\) then, \(A^2=\) ____________ .

  1. A \(25 I\)
  2. B \(- 5 I\)
  3. C \(25 A\)
  4. D \(5 A\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(25 I\)

Step-by-step Solution

Detailed explanation

\( \mathrm{A}^2 = \left[\begin{array}{rrr}0 & 0 & -5 \\ 0 & -5 & 0 \\ -5 & 0 & 0\end{array}\right] \left[\begin{array}{rrr}0 & 0 & -5 \\ 0 & -5 & 0 \\ -5 & 0 & 0\end{array}\right] \) \( \mathrm{A}^2 = \left[\begin{array}{ccc} (0)(0)+(0)(0)+(-5)(-5) & (0)(0)+(0)(-5)+(-5)(0) & (0)(-5)+(0)(0)+(-5)(0) \\ (0)(0)+(-5)(0)+(0)(-5) & (0)(0)+(-5)(-5)+(0)(0) & (0)(-5)+(-5)(0)+(0)(0) \\ (-5)(0)+(0)(0)+(0)(-5) & (-5)(0)+(0)(-5)+(0)(0) & (-5)(-5)+(0)(0)+(0)(0) \end{array}\right] \)