2. suppose a is invertible. a. (25 points) explain why aa is also invertible. b. (25 points) then show that a'=(a^t a^-1) a^t

Answer with explanation:

Part A

It is given that  A is invertible.That is inverse of A exist.

Means, Determinant of A is non zero.

→ |A|≠0

⇒AA=A²

⇒|A²|=A|²

=|A|×|A|

⇒As determinant of A is non zero, so determinant of A² will also be non zero.

⇒|A|² ≠0

Which shows that A² is also invertible.

Part B

We have to prove

→Matrix multiplication is associative.For three matrix A, B and C

(A B)C=A(B C)

→So, this equation is Possible if,

A=A'

its a straight line parallel to the time axis

the correct answer is x/3+10≥32

hope this !