If `A=[[0,1,1],[1,0,1],[1,1,0]]` `B =(1)/(2)[[b+c,c-a,b-c],[c-b,c+a,a-b],[b-c,a-c,a+b]]` then show that `ABA^(-1)` is a diagonal matrix

Show that |1a b_c1b c+a1c a+b|=0

Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .

Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

If A=[[1 ,2,-3],[ 5, 0, 2],[ 1,-1, 1]], B=[[3,-1, 2],[ 4, 2 ,5],[ 2, 0, 3]] and C=[[4, 1, 2],[ 0, 3, 2],[ 1,-2, 3]] , then compute (A+B) and (B - C) . Also, verify that A + (B - C) = (A + B) - C .

Show that |[1,a ,b+c],[1,b, c+a],[1,c ,a+b]|=0 .

If A=[{:(1,-3,2),(2," "0,2):}]" and "B=[{:(2,-1,-1),(1," "0,-1):}] , find a matrix C such that (A+B+C) is a zero matrix.

Prove that |[1+a,1, 1], [1,1+b,1], [1, 1, 1+c]|=a b c(1+1/a+1/b+1/c)=a b c+b c+c a+a b

The value of |{:(1,1,1),(b+c,c+a,a+b),(b+c-a,c+a-b,a+b-c):}| is

If A=[{:(,2,1),(,0,0):}], B=[{:(,2,3),(,4,1):}] and C=[{:(,1,4),(,0,2):}] then show that (i) A(B+C)=AB+AC (ii) (B-A)C=BC-AC .

If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3)] , then A B is equal to (A) B (B) n B (C) B^n (D) A+B