Finding 2 2x2 matrices resulting in -1

[DanceLink]

Homework Statement

Find two different 2×2 matrices (other than ±I) such that A.AT = I.

Definition: I is referring to i^2=-1 axion
AT=Transpose of A

Homework Equations

The Attempt at a Solution

Trying to make matrices on paper so that A times the transpose of A gives me -1 in all rows and columns.

 

[NoMoreExams]

Have you tried just writing out a matrix A with enries a,b,c,d, what would A^T look like then? Then multiply it out and set equal to I?

I'm not sure what you mean by "I is referring to i^2 = -1". I thought by "I" you meant the identity matrix?

 

[DanceLink]

No, there's an axion in mathematics apparently where the variable "i squared" (i^2) equals -1. The reason I wrote a Capital I is because I'm working with a program called Maple. It's the same thing, but in the two matrices that I have to find, I can't use the -1 axion.

Find two different 2×2 matrices (other than ±I) such that A.AT = I.

Sorry for the confusion.

 

[NoMoreExams]

Yes but i^2 = -1 is an imaginary/complex number. You are working with matrices where I refers to the identity matrix.

 

[DanceLink]

...well I feel stupid as all...

lol thanks for clearing that up. ^^;

 

[Mark44]

Yes but i^2 = -1 is an imaginary/complex number. You are working with matrices where I refers to the identity matrix.

No, i^2 is not imaginary. i is, though

 

[NoMoreExams]

No, i^2 is not imaginary. i is, though

Haha, yes.