If A - - 0 c -b- -c 0 a- b -a 0 - and B - - a2 ab ac- ba b2 bc- ca cb c2 - then AB is equal to

The correct option is B [0] A = [ 0 amp; c amp; b; c amp; 0 amp; a; b amp; a amp; 0 ] and B = [ a^2 amp; ab amp; ...

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Multiplication of Matrices

If A = [ 0 ...

Question

If $A = ⎡ ⎢ ⎣ \begin{matrix} 0 & c & - b - c & 0 & a b & - a & 0 \end{matrix} ⎤ ⎥ ⎦$ and $B = ⎡ ⎢ ⎣ \begin{matrix} a^{2} & a b & a c b a & b^{2} & b c c a & c b & c^{2} \end{matrix} ⎤ ⎥ ⎦$ then $A B$ is equal to

[0]

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I

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2 I

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none of these

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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} ⎤ ⎥ ⎦

A B =

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 =

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

(a^{2} + b^{2} - c^{2}) | A | =

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

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

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

t \in C

a d j (t I - A) = t^{2} I + t A + A^{2} + (a^{2} + b^{2} + c^{2}) I

a d j A = A^{2} + (a^{2} + b^{2} + c^{2}) I

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