Let A by an nxn non-singular matrix, then A-1 is the inverse of A. Now
(A-1 )-1 =A
So the answer is yes.
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If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.
if A then B (original) if not A then not B (inverse)
A matrix A is orthogonal if itstranspose is equal to it inverse. So AT is the transpose of A and A-1 is the inverse. We have AT=A-1 So we have : AAT= I, the identity matrix Since it is MUCH easier to find a transpose than an inverse, these matrices are easy to compute with. Furthermore, rotation matrices are orthogonal. The inverse of an orthogonal matrix is also orthogonal which can be easily proved directly from the definition.
of course it does
The original function's RANGE becomes the inverse function's domain.