Can anyone help me solve these? I'm totally stuck...(Thinking)

1. Let A be invertible. Prove that the transpose of A (denoted )

is invertible and

2. Prove that if A is invertible and , then .

Any help on these? (Thinking)

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- Jun 16th 2009, 04:46 PMpaupsersSome basic matrix proofs
Can anyone help me solve these? I'm totally stuck...(Thinking)

1. Let A be invertible. Prove that the transpose of A (denoted )

is invertible and

2. Prove that if A is invertible and , then .

Any help on these? (Thinking) - Jun 16th 2009, 05:06 PMKrizalid

Thus - Jun 16th 2009, 05:13 PMRandom Variable

I have no idea why it's making everything lowercase.

EDIT: I guess it was an issue with Firefox. - Jun 16th 2009, 08:00 PMputnam120
You could also use the fact that .

- Jun 16th 2009, 08:08 PMKrizalid
as far as paupsers knows, since these are basic proofs then the use of determinants wouldn't be valid, though he(she) may clarify this.