Mathematics - Matrices Question with Solution | TestHub

${\left({\text{N}}^{\text{T}}\text{MN}\right)}^{\text{T}}={\text{N}}^{\text{T}}{\text{M}}^{\text{T}}\text{N}$is symmetric if M is symmetric and skew-symmetric if M is skew-symmetric.
${\left(\text{MN}-\text{NM}\right)}^{\text{T}}={\left(\text{MN}\right)}^{\text{T}}-{\left(\text{NM}\right)}^{\text{T}}$
$=\text{NM}-\text{MN}$
$=-\left(\text{MN}-\text{NM}\right)$
skew symmetric
${\left(\text{MN}\right)}^{\text{T}}={\text{N}}^{\text{T}}{\text{M}}^{\text{T}}$
$\; \; \; \; = \text{NM}$
$\ne \text{MN}$hence not correct
Standard result is
$\text{adj}\left(\text{MN}\right)=\left(\text{adj N}\right)\left(\text{adj M}\right)$
$\ne \left(\text{adj M}\right)\left(\text{adj N}\right)$