Suppose $$A=\pmatrix{1&2&3&4&5\\2&3&4&5&6}$$ Find $\det(A^TA)$.

I know exactly how to calculate it by writing it as a $5\times5$ matrix. But how to calculate it smartly?

marked as duplicate by amd, amWhy linear-algebra Aug 19 at 22:55

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

up vote 30 down vote accepted
  • Rank of $A$ is $2$, hence $A^TA$ cannot be rank $5$ and it must be singular.

  • Hence the determinant must be $0$.

Not the answer you're looking for? Browse other questions tagged or ask your own question.