Let A be a skew-symmetric matrix of order 3. What is the value of (4A^4)- (3A^3)+ (2A^2)- (A)+ (-I) where I is the identity matrix of order 3?

NDA 2023 Mathematics question

Let be a skew-symmetric matrix of order 3. What is the value of

-+-(A)+(-I)

where is the identity matrix of order 3?

Answer: (A)

The determinant of a skew-symmetric matrix of odd order is zero, so . Then , $ =

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Question ID VK-029658