If then determinant of [A] is

Engineering

Mathematics

Introduction to Determinants

Properties of Determinant

Question

If $A = [\begin{array}{cc} 0 & 1 \\ - 1 & 0 \end{array}]$ then determinant of [A] is

– 1

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Determinants of a 2 × 2 matrix is given by:

A = [\begin{array}{cc} a & b \\ c & d \end{array}]

Det(A) = ad – bc

Hence using this above property:

A = [\begin{array}{cc} 0 & 1 \\ - 1 & 0 \end{array}]

, then

Det(A) = 0 × 0 – 1 × (– 1) = 0 + 1 = 1