If `A=[(3,1,-1),(0,1,2)]`, then show that `A A'` is a symmetric matrix.

If A=[[3m,-4],[1,-1]] , show that (A-A^T) is skew symmetric matrix, where A^T is the transpose of matrix A.

If A=[3-41-1], show that A-A^(T) is a skew symmetric matrix.

If A=[[3,4],[5,1]] , show that A-A^T is a skew symmetric matrix, where A^T denotes the transpose of matrix A

for the matrix A=[{:(1,5),(6,7):}], verify that : (I) (A+A') is a symmetric matrix. (ii) (A-A') is a skew symmetric matrix.

If A=[[3,-47,8]], show that A-A^(T) is a skew symmetric matrix where A^(T)1 s the transpose of matrix A

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.

Show that the matrix, A=[(0,1,-1),(-1,0,1),(1,-1,0)] is a skew - symmetric matrix.

If A=[[4,1],[5,8]] , show that A+A^T is symmetric matrix, where A^T denotes the transpose of matrix A

Matrices of order 33 are formed by using the elements of the set A={-3,-2,-1,0,1,2,3} then probability that matrix is either symmetric or skew symmetric is

If matrix A=[(0,1,-1),(4,-3,4),(3,-3,4)]=B+C , where B is symmetric matrix and C is skew-symmetric matrix, then find matrices B and C.