If then (a2 + b2 – c2) |A| =

Engineering

Mathematics

Special Type of Square Matrices

Introduction to Determinants

Properties of Determinant

Question

If $A = |\begin{matrix} 0 & c & - b \\ - c & 0 & a \\ b & - a & 0 \end{matrix}|$ then (a² + b² – c²) |A| =

a + b + c

abc

(a³ + b³ + c³)

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|A| = 0 × (a²) – c(– ab) – b(ac)

= 0 + abc – abc

= 0