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GUJCET · Maths · Matrices
If \(A=\left[\begin{array}{lll}3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3\end{array}\right]\) then, \(A^3=\) ____________
- A 243 A
- B 81 A
- C 27 A
- D 729 A
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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