Determinant Properties

Algebra Level 3

If A is a 3*3 matrix where |A| = 5, then what is the value of |5 A 1 A^{-1} |


The answer is 25.

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1 solution

Mahmoud Ayyad
Oct 28, 2015

| 5 A 1 A^-1 | = 5 3 5^3 * | A 1 A^-1 | = 5 3 5^3 / |A| = 5 3 5^3 / 5 = 5 2 5^2 = 25

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