Using the properties of determinants, find the value of

Engineering

Mathematics

Special Type of Square Matrices

Introduction to Determinants

Properties of Determinant

Question

Using the properties of determinants, find the value of

∣ \begin{array}{ccc} 0 & a & - b \\ - a & 0 & - c \\ b & c & 0 \end{array} ∣

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Let $∆ = ∣ \begin{array}{ccc} 0 & a & - b \\ - a & 0 & - c \\ b & c & 0 \end{array} ∣$
Expanding along first column,
Δ = a(0 + bc) + b(– ac – 0) = abc – abc = 0