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Inverse of a Matrix

Multiplicatio...

Question

Multiplication of two matrices is not commutative, but the value of trace of AB will be equal to trace of BA.

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Solution

$[\begin{matrix} a & b c & d \end{matrix}] [\begin{matrix} e & f g & h \end{matrix}] [\begin{matrix} a e + b g & a f + b h c e + d g & e f + h d \end{matrix}] T r a c e (A B) = a e + b g + c f + h d [\begin{matrix} e & f g & h \end{matrix}] [\begin{matrix} a & b c & d \end{matrix}] [\begin{matrix} e a + c f & e b + d f a g + c h & g b + h d \end{matrix}] T r a c e (B A) = e a + c f + h b + h d = e a + b g + c f + h d = T r a c e (A B)$

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