If $\mathrm{A}$ and $\mathrm{B}$ are square matrices of the same order such that $\mathrm{A}=-{\mathrm{B}}^{-1}\mathrm{A}\mathrm{B}$, then ${\left(\mathrm{A}+3\mathrm{B}\right)}^2$ is equal to

• A

  $\mathrm{A}+3\mathrm{B}$
• Correct answer
  B

  ${\mathrm{A}}^2+9{\mathrm{B}}^2$
• C

  ${\mathrm{A}}^2+6\mathrm{A}\mathrm{B}+\mathrm{A}{\mathrm{B}}^2$
• D

  $\mathrm{O}$

Hence, the correct answer is option: 'B'.