Two matrices A and B of same order 2 are said be inverses to each other if AB=BA=I, where ‘I’ is the unit matrix of same order 2.
Here, A is called inverse of B and B is called inverse of A.
i.e. A= B–1 and B= A-1.
Note 1:
From the above definition, we have
A A-1 = A-1 A = I and
B B-1 = B-1 B = I.
Note 2:
b) The inverse of a 2×2 matrix exists (or A is invertible) only if ad-bc≠0.
c) Inverse does not exist for a rectangular matrix.
Properties:
The inverse of a matrix has the following properties.
a) Inverse of a matrix is unique, if it exists.
b) (AB)-1 = B-1 A-1
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