The inverse of a rotation matrix represents a rotation in the opposite direction, by the same angle, about the same axis.
Since M-1M = I, M-1(Mv) = v. Thus, any matrix inverse will "undo" the transformation of the original matrix.
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From Wolfram MathWorld: The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A-1 such that AA-1=I where I is the identity matrix.
The fact that the matrix does not have an inverse does not necessarily mean that none of the variables can be found.
A rectangular (non-square) matrix.
You can factorize the matrix using LU or LDLT factorization algorithm. inverse of a diagonal matrix (D) is really simple. To find the inverse of L, which is a lower triangular matrix, you can find the answer in this link.www.mcs.csueastbay.edu/~malek/TeX/Triangle.pdfSince (A T )-1 = (A-1 )T for all matrix, you'll just have to find inverse of L and D.
I could do that if you gave me the original matrix.