JEE Main · MathematicsHard

$If A is a skew-symmetric matrix of order 3, then the value of det (A^{4}) is always equal to:$

A. $1$
B. $0$
C. $A^{2}$
D. $None of these$

Show correct answer & step-by-step solution

Correct answer: B — $0$

Solution

For any skew-symmetric matrix A of odd order n, det (A) = det (A^{T}) = det (- A) = (- 1)^{n} det (A) = - det (A), implying det (A) = 0 . Thus, det (A^{4}) = 0^{4} = 0 .

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