0 votes 0 votes Consider the matrices $A=\begin{pmatrix} 0 & 0 & 0 & 0 & 15 \\ 0 & 0 & 0 & 13 &14 \\ 0 & 0 & 10 & 11 & 12 \\ 0 & 6 & 7 & 8 & 9 \\ 1 & 2 & 3 & 4 & 5 \end{pmatrix} \text{ and}\; B=\begin{pmatrix} 5 & 4 & 3 & 2 & 1 \\ 9 & 8 & 7 & 6 & 0 \\ 12 & 11 & 10 & 0 & 0 \\ 14 & 13 & 0 & 0 & 0 \\ 15 & 0 & 0 & 0 & 0 \end{pmatrix}$ Which of the following hold true? $|A|=|B|$ $\text{trace}(A)=\text{trace}(B)$ $|A|=-|B|$ $\text{trace}(AB)=\text{trace}(BA)$ Others cmi2020-datascience + – soujanyareddy13 asked Jan 29, 2021 edited Feb 12, 2021 by soujanyareddy13 soujanyareddy13 259 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes Solution: (A), (B) and (D) are true. The given matrices are obtained from $\begin{pmatrix} 1&2&3&4&5 \\0&6&7&8&9\\0&0&10&11&12\\0&0&0&13&14\\0&0&0&0&15 \end{pmatrix}$ by $10$ row and$10$ column exchanges respectively. LasyaReddy07 answered Feb 1, 2021 LasyaReddy07 comment Share Follow See all 0 reply Please log in or register to add a comment.