If the eigenvalue of a square matrix of order 2 is 1, - 1 and a * is its adjoint matrix, then the value of determinant | a * - 2e | is?

If the eigenvalue of a square matrix of order 2 is 1, - 1 and a * is its adjoint matrix, then the value of determinant | a * - 2e | is?

If the eigenvalue of a is 1, - 1, then | a | = 1 * (- 1) = - 1
Then a * = | a | * a ^ (- 1) is - 1,1
Then the eigenvalues of a * - 2E are - 3, - 1
So | a * - 2e | = (- 3) * (- 1) = 3

Let a be a square matrix of order 3, and the determinant of a = a ≠ 0, and a * be the adjoint matrix of a, then how much is a * equal to? Please write down the calculation process, thank you

Knowledge point: | a * | = | a | ^ (n-1), where n is the order of A
So | a * | = | a | ^ (3-1) = a ^ 2

Let a be a square matrix of order 3, a * be the adjoint matrix of a, and a = 2, then the determinant (1 / 4 * a) ^ - 1 - 3A * is = - 4

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