The inverse of a matrix A is a matrix that, when multiplied by A results in the identity.
An identity matrix is a matrix equivalent to 1.
There is no concept of dividing by a matrix but, we can multiply by an inverse, which achieves the same thing.
Formula to calculate inverse matrix of a 2 by 2 matrix.
We begin by finding the determinant of the matrix.
Swap the positions of the elements in the leading diagonal.
And put a negative sign in front of the elements in the other diagonal.
Lastly, multiply the resultant matrix by 1 divided by the determinant.
Example:
Find the inverse of the following matrix.
We begin by finding the determinant of the matrix.
Therefore, the determinant of the matrix is -5.
Then we swap the positions of the elements in the leading diagonal and put a negative sign in front of the elements on the other diagonal.
And lastly, multiply the resultant matrix by 1 divided by the determinant.
