If a 3 andtimes; 3 square matrix A has the eigen values 3, 4 and 5, then the determinant of adjoint of matrix A isCorrect answer is '3600'. Can you explain this answer?

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If a 3 × 3 square matrix A has the eigen values 3, 4 and 5, then the determinant of adjoint of matrix A is

Correct answer is '3600'. Can you explain this answer?

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If a 3 × 3 square matrix A has the eigen values 3, 4 and 5, then...

Given that, Eigen values of a matrix A = 3, 4 and 5
From the properties of Eigen values, determinant of a matrix is equal to the product of their Eigen values.
⇒ |A| = 3 × 4 × 5 = 60
|Adj A| = |A|^n-1= |A|² = 60² = 3600

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If a 3 × 3 square matrix A has the eigen values 3, 4 and 5, then the determinant of adjoint of matrix A isCorrect answer is '3600'. Can you explain this answer?

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