Question

Give an example of a matrix which is its own inverse (that is, where A^-1 = A)

Answer 1

the identity matrices

Answer 2

The answer is Many answers ex:
-10 9
-11 10

But I don't understand... how did they get this answer?

Answer 3

What about the identity matrices?

Answer 4

the inverse of an identity is an identity itsself. and an identity times any matrix gives the same matrix. so any identity matrix is a solution

Answer 5

no thats wrong

Answer 6

\[\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right]\]

Answer 7

I know the identity matrix is
1 0
0 1

Answer 8

oops sorry my bad a mistake in haste:/

Answer 9

But I don't understand how to do this :(

Answer 10

I understand what an identity matrix is, but I don't know how to come up with a matrix myself

Answer 11

that is its own inverse

Answer 12

I guess it's any matrix that has 1 as its determinant?

Answer 13

-1

Answer 14

\[A=A^{-1}.\]\[\implies \frac{A}{A^{-1}}=1I.\]\[\implies A \times A^1=A \times A=A^2=1I.\]\[\color{red}{\implies A= \sqrt{1I}=1\sqrt{I}=\sqrt{I}=I.}\]Which is an identity matrix.