Let be a real number. Consider the matrix A = pmatrix & 0 & 1 2 & 1 & -2 3 & 1 & -2 pmatrix . If A^7 - ( - 1)A^6 - A^5 is a singular matrix, then the value of 9 is _____.

JEE Advanced 2022 Mathematics question

Let be a real number. Consider the matrix

A = .

If is a singular matrix, then the value of is .

Answer: 3

. . So the matrix is singular iff or is an eigenvalue of . The characteristic

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Question ID VK-034013