CBSE Class 12-science Answered

in this basically you need to show that square of a skew symmetric matrix is symmetric because then, all the even powers can be shown to be symmetric. Next, you have to show that the product of a skew symmetric and a symmetric matrix is skew symmetric, so then you can show that all odd powers of a skew symm matrix are skew symm. This can be done as follows. If A is a skew symmetric matrix , show that, A*A is symmetric. Then also show that (A*A)*A=a symmetric matrix * a skew symm matrix is skew symm.Then every even power being a symm matrix, its multiplication with A will give a skew symm matrix.