Question

prove that sum of two skew symmetric matrices is a skew symmetric matrix

Answer 1

Given: Two skew symmetric matrices.

To find: Prove that sum of two skew symmetric matrices is a skew symmetric matrix.

Solution:

• As we have given the two skew symmetric matrices, so let the matrices be A and B.

• Now we know that transpose of a matrix is equal to the matrix itself with a negative sign, which means:

                A' = -A and B' = -B

• Now, taking transpose of A+B, we get:

               (A+B)' = A'+B'

                          = −A−B

              (A+B)' = −(A+B)

               Hence proved

Solutions:

               So as proved above that sum of two skew symmetric matrices is always skew symmetric matrix.