If `A=[[0 ,c,-b],[-c, 0, a],[ b, -a, 0]]` and `B=[[a^2, ab, ac],[ ab, b^2 , bc],[ ac ,bc, c^2]]` , show that `A B=B A=O_3xx3` .

|[x^2+a^2,ab,ac] , [ab,x^2+b^2,bc] , [ac,bc,x^2+c^2]|=

If A=[{:(0," "c,-b),(-c," "0," "a),(b,-a," "0):}]" and "B=[{:(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2)):}] , show that AB is a zero matrix.

If A=[{:(0,c,-b),(-c,0,a),(b,-a,0):}] and B=[{:(a^(2),ab,ac),(ab,b^(2),bc),(ac,bc,c^(2)):}] , then (A+B)^(2)=

abs([-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]) = 4a^2.b^2.c^2

Prove that |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]|=1+a^2+b^2+c^2

the determinant Delta=|[a^2+x, ab, ac] , [ab, b^2+x, bc] , [ac, bc, c^2+x]| is divisible by

If A=[[0, 6, 7], [-6, 0, 8], [ 7,-8, 0]] , B=[[0, 1, 1],[ 1, 0, 2],[ 1, 2, 0]] , C=[[2], [-2] , [3]] Calculate AC, BC and (A + B)C . Also, verify that (A + B)C = A C + B C

If ∣ -a a^2 ab ac ab -b^2 bc ac bc -c^2 | = ka^2b^2c^2 , then k is equal to

Prove that: |-a^2 ab ac ba -b^2 bc ac bc c^2| =4a^2b^2c^2 .

Find the product of the following two matrices [(0,c,-b),(c,0,a),(b,-a,0)] and [(a^2,ab,ac),(ab,b^2,bc),(ac,bc,c^2)] .