Let B=
0 1
1 0
Find B if it is to the negative one power. (Its supposed to be a matrix, but I don't know how to write the brackets on the computer)
it is supposed to be
0, 1
1, 0
not 01 and 10. sorry
In other words find the inverse matrix?
0,1
1,0
times
a,b
c,d
equals identity matrix
1,0
0,1
then
c = 1
d = 0
a = 0
b = 1
so
0,1
1,0
In other words, it is its own inverse
here is a link
http://www.mathwords.com/i/inverse_of_a_matrix.htm
To find the inverse of a given matrix B, you need to follow these steps:
1. Compute the determinant of the matrix B.
The determinant of a 2x2 matrix [a, b; c, d] is given by ad - bc.
In this case, for matrix B = [0, 1; 1, 0], the determinant is (0 * 0) - (1 * 1) = -1.
2. Check if the determinant is zero.
If the determinant is zero, then the matrix does not have an inverse. However, if the determinant is non-zero, which is the case here (-1), then the matrix has an inverse.
3. Swap the elements along the main diagonal (top-left to bottom-right).
For a 2x2 matrix, swapping the elements along the main diagonal is simply interchanging the top-left and bottom-right elements.
In our case, B swapped would be [0, 1; 1, 0].
4. Negate the elements outside the main diagonal.
Negating the elements outside the main diagonal involves changing the signs of the elements.
So, negating the elements of B swapped, we get [-0, -1; -1, -0], which simplifies to [0, -1; -1, 0].
Therefore, the inverse of B, denoted as B^-1, is [0, -1; -1, 0].