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If A={bmatrix}1 & 1 1& 1{bmatrix}, then A^{100} is equal to.

Question

If $A = [1111]$ , then $A^{100}$ is equal to.

2^{100} A

2^{99} A

100 A

299 A

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Henry Discussed

A = [1111]

, then

A^{100}

is equal to.

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Given,

A = [1111]

∴ A^{2} = A \cdot A = [1111] [1111]

= 2 [1111] = 2 A

Now,

A^{4} = A^{2} \cdot A^{2} = 2 A \cdot 2 A

= 4 A^{2} = 4 \times 2 A

= 8 A = 2^{3} A

Similarly,

A^{8} = 2^{7} A

∴ A^{100} = 2^{99} A

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