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If A = [ 3 7 1 2 ], then the value of the determinant | A^2013 − 3A^2012 | 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 |A^n| = |A|^n. In this case, the determinant of A is -1, so |A^2013| = (-1)^2013 = -1 and |3A^2012| = 3^2012 * |A| = 3^2012 * (-1). Therefore, the determinant of the expression simplifies to -1 - 3^2012, which evaluates to -7.

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