If A is 3 * 3 show symmetric matrix then |A| = ?

Engineering

Mathematics

Introduction to Determinants

Question

– 1

N.O.T.

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Let $A = [\begin{array}{ccc} 0 & a & b \\ - a & 0 & c \\ - b & - c & 0 \end{array}]$

$A^{⊤} = [\begin{array}{ccc} 0 & - a & - b \\ a & 0 & - c \\ b & c & 0 \end{array}]$

A^T = – A

|A| = 0(0 + c²) – a(0 + bc) + b(ac – 0)

= – abc + abc

= 0

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