Math Help - find matrices that ..

1. find matrices that ..

hi everyone. im having some trouble with this question...

thank you!

EDIT: I think I found the answer ... for part a) would it be

0 0 1
0 1 0
1 0 0

(so an identity matrix flipped horizontally?)

2. Originally Posted by finalfantasy
EDIT: I think I found the answer ... for part a) would it be
0 0 1
0 1 0
1 0 0
Not according to my CAS. Look again at the third power it is back to the original.
But try $
\left( {\begin{array}{ccc}
0 & 0 & 1 \\
1 & 0 & 0 \\
0 & 0 & 0 \\ \end{array} } \right)$

3. Thanks!

would i use the property of determinants to solve part b? (this assignment is about determinants)

4. Originally Posted by finalfantasy
this assignment is about determinants
As such can you use $\left| {AB} \right| = \left| A \right|\left| B \right|$ to prove that $\left| {A^k } \right| = \left| A \right|^k$?
If you can, then that answers your question.

5. hm .. what i ended up doing was stating that if B inverse exists, then det (B) cannot equal zero.

i used the example from part one to illustrate that, and the det. was zero therefore there was no inverse. can that suffice as answer?