If then AB =

Engineering

Mathematics

Algebra of Matrices

Special Type of Square Matrices

Introduction to Determinants

Question

If $A = [\begin{array}{ccc} 0 & c & - b \\ - c & 0 & a \\ b & - a & 0 \end{array}], B = [\begin{array}{ccc} a^{2} & ab & ac \\ ba & b^{2} & bc \\ ca & cb & c^{2} \end{array}]$ then AB =

None of these

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$AB = [\begin{array}{ccc} 0 & c & - b \\ - c & b & a \\ b & - a & 0 \end{array}] [\begin{array}{ccc} a^{2} & ab & ac \\ ba & b^{2} & bc \\ ca & cb & c^{2} \end{array}]$

$= [\begin{array}{ccc} abc - abc & b^{2} c^{1} - b^{2} c & {bc}^{2} - {bc}^{2} \\ - a^{2} c + a^{2} c & - abc + abc & - {ac}^{2} + {ac}^{2} \\ a^{2} b - a^{2} b & {ab}^{2} - {ab}^{2} & abc - abc \end{array}]$

$= [\begin{array}{ccc} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] = 0 \Rightarrow (A)$