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GUJCET · Maths · Matrices

જો \(A=\left[\begin{array}{lll}3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3\end{array}\right]\) તો \(A^3=\)_________

  1. A 243 A
  2. B 81 A
  3. C 27 A
  4. D 729 A
Verified Solution

Answer & Solution

Correct Answer

(B) 81 A

Step-by-step Solution

Detailed explanation

\(A^2 = \left[\begin{array}{lll}3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3\end{array}\right] \left[\begin{array}{lll}3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3\end{array}\right] = \left[\begin{array}{lll}27 & 27 & 27 \\ 27 & 27 & 27 \\ 27 & 27 & 27\end{array}\right] = 9A\) \(A^3 = A^2 \cdot A = (9A) \cdot A = 9A^2\)
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