# Finding 2 2x2 matrices resulting in -1

In summary, The task is to find two different 2×2 matrices, other than ±I, such that their product with their transpose equals the identity matrix. The definition of I in this context is the identity matrix and not the imaginary number i^2 = -1. The attempt at a solution involves writing out matrices A with entries a, b, c, and d and finding the transpose of A, then multiplying them and setting them equal to I. The confusion was caused by the mention of i^2 = -1, which is an imaginary/complex number, but not relevant to the task.

## 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

## 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.

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?

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.

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

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

lol thanks for clearing that up. ^^;

NoMoreExams said:
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

Mark44 said:
No, i^2 is not imaginary. i is, though

Haha, yes.

## 1. How do I find 2 2x2 matrices resulting in -1?

To find 2 2x2 matrices resulting in -1, you can use the following formula:
[1 1]
[-1 -1]
[-1 1]
[1 -1]

## 2. Can I use any numbers to create the matrices?

Yes, you can use any numbers as long as they follow the pattern of the formula mentioned above. For example, you can use [2 3] and [-2 -3] to create the matrices.

## 3. Is there a specific order in which I should place the numbers in the matrices?

Yes, the order of the numbers in the matrices should follow the pattern of [a b] and [c d], where a and b are the same and c and d are the opposite of a and b.

## 4. How can I check if my matrices result in -1?

To check if your matrices result in -1, you can simply multiply them together using the matrix multiplication method and check if the resulting matrix has -1 as its value.

## 5. Are there any other methods to find 2 2x2 matrices resulting in -1?

Yes, there are other methods such as using a system of equations to solve for the values of the matrices or using the inverse of a matrix to find the desired result. However, the formula mentioned above is the most efficient way to find the matrices resulting in -1.

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