23 September 2014
1) Show that every square matrix is uniquely expressible as the sum of a symmetric and a skew-symmetric matrix.
2) If A is a square matrix of order n, prove that
| Adj (Adj A) | =|A|(n-1)ᴧ2
3) Find the rank of the matrix
2 -2 0 6
4 2 0 2
A= 1 -1 0 3
1 -2 1 2
by reducing it to normal form.
