Question

If A is a skewsymmetric matrix of 3×3. Prove that detA=0

Answer 1

If A is a skew symmetric matrix then according to, Properties of Determinants {det() stands for Determinant of}

det(A) = det(AT) where AT stands for Transpose

of Matrix A

& for all skew symmetric matrices A = (-AT)

ð

det(A) = det(-A)

ð

2det(A) = 0

ð

det(A) = 0 [PROVED]