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If A = [ 3 7 1 2 ], then the value of the determinant | A²⁰¹³ − 3A²⁰¹² | is equal to

1. 8
2. −8
3. 9
4. −7

Correct answer: −7

Solution

The determinant of a matrix raised to a power can be calculated using the property that |Aⁿ| = |A|ⁿ. In this case, the determinant of A is -1, so |A²⁰¹³| = (-1)²⁰¹³ = -1 and |3A²⁰¹²| = 3²⁰¹² * |A| = 3²⁰¹² * (-1). Therefore, the determinant of the expression simplifies to -1 - 3²⁰¹², which evaluates to -7.

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