KCET2024MathematicsMatrices

If A= ( array ll 1 & 1 1 & 1 array ) , then A¹⁰ is equal to

Options

A2^8 A
B2^9 ~A
C2¹⁰ A
D2¹¹ A

Correct answer

B. 2^9 ~A

Step-by-step solution

A= ( array ll 1 & 1 & 1 array ) , A^2= ( array ll 1 & 1 1 & 1 array ) ( array ll 1 & 1 1 & 1 array )= ( array ll 1+1 & 1+1 1+1 & 1+1 array )= ( array ll 2 & 2 2 & 2 array )=2 ( array ll 1 & 1 1 & 1 array )=2 A A^3= ( array ll 2 & 2 2 & 2 array ) ( array ll 1 & 1 1 & 1 array )= ( array ll 2+2 & 2+2 2+2 & 2+2 array )= ( array ll 4 & 4 4 & 4 array )=4 ( array ll 1 & 1 1 & 1 array )=4 A

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