# matrix proof 1

• Jan 24th 2009, 12:52 PM
nerdo
matrix proof 1
Can some 1 please help me with this as i really hate and sturggle doing matrix proof (Angry)

Attachment 9795
• Jan 24th 2009, 01:09 PM
GaloisTheory1
Quote:

Originally Posted by nerdo
Can some 1 please help me with this as i really hate and sturggle doing matrix proof (Angry)

Attachment 9795

for b, A =
[1 0]
[0 1]
B =
[0 1]
[1 0]
Then AB =/= BA

so for c, no, by part b.
• Jan 24th 2009, 01:18 PM
nerdo
Once again thanks for the help
• Jan 25th 2009, 01:13 PM
nerdo
Quote:

Originally Posted by GaloisTheory1
for b, A =
[1 0]
[0 1]
B =
[0 1]
[1 0]
Then AB =/= BA

so for c, no, by part b.

Sorry but i think u got this wrong as AB=BA if u calculate it.
• Jan 25th 2009, 01:44 PM
mr fantastic
Quote:

Originally Posted by GaloisTheory1
for b, A =

[1 0]

[0 1]

B =

[0 1]

[1 0]

Then AB =/= BA

so for c, no, by part b.

Quote:

Originally Posted by nerdo
Sorry but i think u got this wrong as AB=BA if u calculate it.

Correct. The example given does not answer the question. Also, since one of them is the identity matrix they obviously commute .....

Surely it's not too hard to find two matrices that satisfy the requirements of (b). In fact, I bet you could choose to 2x2 matrices at random that would work ..... Then the answer to c is obvious.

As for (a), two trivial matrices that satisfy the requirements are

[1, 1]
[1, 1]

[2, 2]
[2, 2]

It is not too hard to construct less trivial examples .....
• Jan 25th 2009, 01:48 PM
nerdo
Quote:

Originally Posted by mr fantastic
Correct. The example given does not answer the question. Also, since one of them is the identity matrix they obviously commute .....

Surely it's not hard too find two matrices that satisfy the requirements of (b). In fact, I bet you could choose to 2x2 matrices at random that would work. Then the answer to c is obvious.

As for (a), two trivial matrices that satisfy the requirements are

[1, 1]
[1, 1]

[2, 2]
[2, 2]

It is not too hard to construct less trivial examples .....

Thanks for the help, i hav know actually managaed to solve this question