If A- 0 c -b- -c 0 a- b -a 0 -B- a 2 ab ac- ba b 2 bc- ca cb c 2 - then AB-

The correct option is A O AB=[ 0 amp; c amp; b; c amp; b amp; a; b amp; a amp; 0 ][ a^ 2 amp; ab amp; ac; ba ...

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Multiplication of Matrices

If A=[ 0 c ...

Question

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

O

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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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