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what is a 3x3 invertible matrix?

Mathematics
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Are you OK with what a 3x3 matrix is?
do you want a formal definition or a solved example showing all steps of inverting a 3x3 matrix?
a solved example would be great

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Other answers:

ok
which means its determinant cant be 0?
yest i will show you the full steps
consider the following matrix
PLZ continue
\[A=\left[\begin{matrix}1 & -2 & 0\\ 3& 1 & 5\\ -1 & 2 & 3\end{matrix}\right]\]
Step one: \[A^T\]
which means transpose of rows and columns of A
\[A^T=\left[\begin{matrix}1 & 3 & -1\\ -2& 1 & 2\\ 0 & 5 & 3\end{matrix}\right]\]
Step Two: find the adjoint or adjugate of A, which implies that we replace each element by their cofactor...
If P = \begin{bmatrix} a &b &c \\ d &e &f \\ g &h &i \end{bmatrix}
now please concentrate on this step it is simple but requires a bit of accuracy
And P^4=2P how can we find P
let's finish this first part then i will come to the 2nd question, you asked me first for a numerical example
so we need to find adjA
I know how to find a inverse matrix. So, can u plz do the 2nd question
ok sure
any idea?
yes sorry am on the phone, but just a quick hint for P^n we use the principle of induction
i will show you shortly
@mathsmind why is taking so long?
sorry back, am at work
now P^4 means you are multiplying your matrix by itself 4 times.
yep
you know how to multiply the, it would be PP=P^2, then P^2P=P^3. then P^3P=P^4
But it would be really long
well this is the world of Matrices...
are you thinking of algebraic operation on matrices such as taking the inverse of 2P
or subtracting p^4-2P=0 in order to find the new P?
Isn't there any short way
have you done hermitian matrices...
nope
listen can we kindly finish this tonight because it is 5 am and i need to go ...
okay
i will provide you with full solution even if you are not online ok
see ya tonight
lol, you still here? I thought you got help
No
can u do it?
Short way
I haven't done matrices yet: I am stuck with number theory at the moment.
Nope.
http://www.wikihow.com/Inverse-a-3X3-Matrix
@looser there are many matrices such that P^4=2P but only one is invertible which is |dw:1361026643638:dw|

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