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Null Matrix

If A and B ar...

Question

If A and B are matrices given below :
A = $⎡ ⎢ ⎣ \begin{matrix} 0 & c & - b - c & o & a b & - a & 0 \end{matrix} ⎤ ⎥ ⎦$ and B = $⎡ ⎢ ⎣ \begin{matrix} a^{2} & a b & a c a b & b^{2} & b c a c & b c & c^{2} \end{matrix} ⎤ ⎥ ⎦$
then AB is a unit matrix . Is this statement true?

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Solution

False
Correct is that AB is null matrix.

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A = ⎡ ⎢ ⎣ \begin{matrix} 0 & c & - b - c & 0 & a b & - a & 0 \end{matrix} ⎤ ⎥ ⎦

B = ⎡ ⎢ ⎣ \begin{matrix} a^{2} & a b & a c a b & b^{2} & b c a c & b c & c^{2} \end{matrix} ⎤ ⎥ ⎦,

A B =

A = ⎡ ⎢ ⎣ \begin{matrix} o & c & - b - c & o & a b & - a & o \end{matrix} ⎤ ⎥ ⎦ a n d

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A = ⎡ ⎢ ⎣ \begin{matrix} 0 & c & - b - c & 0 & a b & - a & 0 \end{matrix} ⎤ ⎥ ⎦

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A = ⎡ ⎢ ⎣ \begin{matrix} 0 & c & - b - c & 0 & a b & - a & 0 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} a^{2} & a b & a c b a & b^{2} & b c c a & c b & c^{2} \end{matrix} ⎤ ⎥ ⎦

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A = ⎡ ⎢ ⎣ \begin{matrix} a^{2} & a b & a c a b & b^{2} & b c a c & b c & c^{2} \end{matrix} ⎤ ⎥ ⎦

a^{2} + b^{2} + c^{2} = 1

A^{2} =

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