the transpose of null space of A is equal to orthogonal complement of A
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int sym_test(const **a,int n){ int i,j,sym; i=1;j=0;sym=1; while(sym && i<n){ if ( a[i][j] != -[j][i] ) sym=0; else if (j<i-1) ++j; else ++i,y=0; } return sym; }
Multiply it by the identity matrix.
They both cannot be
If the product of two matrices is an identity matrix then, one matrix is inverse of the other. i.e. AB = I then, A = B-1 and B = A-1Inverse of matrix can be found by using these two results:A = AI and A = IA.By using these results inverse of a matrix can be found by applying same elementary row or column operation on both sides. A on R.H.S. remains as it is.