# Is this tensor identity true?

If We have two vectors $\boldsymbol{a}$ and $\boldsymbol{b}$ and a symmetric positive definite Matrix $\boldsymbol{M}$ I was wondering if the expression $((\boldsymbol{a}\times \boldsymbol{b}) \cdot \boldsymbol{M}) \times \boldsymbol{a}$ was equivalent to $(\boldsymbol{a}\times \boldsymbol{b} \times \boldsymbol{a}) \cdot \boldsymbol{M}$ thanks in advance for the help!

• What is $a\times b\times a$? – Peter Franek Mar 11 '15 at 14:31
• Should that be $a \otimes b$ and $a \otimes b \otimes a$? – Omnomnomnom Mar 11 '15 at 14:32
• It's the same of $(\boldsymbol{a}\times \boldsymbol{b}) \times \boldsymbol{a}$ which is itself equal to $\boldsymbol{a}\times (\boldsymbol{b} \times \boldsymbo{a})$ – SSC Napoli Mar 11 '15 at 14:38
• @Omnomnomnom: you cancelled your answer but you're not posting a corrected one? – SSC Napoli Mar 11 '15 at 18:25