We want to get an expression for B in terms of A and C. So first we rewrite the expression in terms of a skew symmetric matrix [~A] such that: Since it's always true that B * B^(-1) * B = B (with B^(-1) the pseudo-inverse of B) if A is 2x2 of |a b| |c d| then A(inverse) = |d -c| |-b a| * 1/det(A) A symmetric for 2x2 is |a b| |b d| so inverse would be |d -b| |-b a| * 1/det(A) which is also symmetric. In linear algebra, a real symmetric matrix represents a self-adjoint operator over a real inner product space. If is a real skew-symmetric matrix, then + is invertible, where is the identity matrix. Solution for Skew-symmetric matrix. An antisymmetric matrix is a square matrix that satisfies the identity A=-A^(T) (1) where A^(T) is the matrix transpose. and the required skew-symmetric matrix is. A great virtue of MATLAB (ok, almost any programming language) is the ability to write functions that do what you want. For any square matrix A, (A + A T ) is a symmetric matrix (A â A T ) is a skew-symmetric matrix Inverse of a matrix For a square matrix A, if AB = BA = I Then, B is the inverse â¦ The elements on the diagonal of a skew-symmetric matrix are zero, and therefore its trace equals zero. Transpose and Inverse; Symmetric, Skew-symmetric, Orthogonal Matrices Definition Let A be an m × n matrix. Yup, the phrase "each non-zero element".