The trace of a square matrix is defined to be the sum of its diagonal entries. If A is a 2 2 matrix such that the trace of A is 3 and the trace of A^3 is -18, then the value of the determinant of A is _____

JEE Advanced 2020 Mathematics question

The trace of a square matrix is defined to be the sum of its diagonal entries. If is a matrix such that the trace of is 3 and the trace of is , then the value of the determinant of is

Answer: 5

Solution

Let be the eigenvalues of . Then , and . Using 1^32^3$ =

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Question ID VK-033825