If A = 2 3 - 1 - 2 and B = ∑ r = 1 10 A r , then the value of det B is equal to

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Question: Answered & Verified by Expert

If

A = [\begin{array}{l} 2 & 3 \\ - 1 & - 2 \end{array}]

and

B = \sum_{r = 1}^{10} A^{r}

, then the value of det

(B)

is equal to

MathematicsDeterminantsJEE Main

Solution:

2195 Upvotes Verified Answer

The correct answer is: 0

Note

A^{2} = Ι \Rightarrow A^{n} = Ι

(if

n

is even) &

A^{n} = A

(if

n

is odd)
So,

B = 5 (A + Ι) = 5 [\begin{array}{l} 3 & 3 \\ - 1 & - 1 \end{array}] \Rightarrow |B| = 0

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