If `A=[[0,q,r],[p,(a-b),(b-c)],[0,0,(c-b)]]` , then find `|A|`

If a!=p,b!=q,c!=r and det[[p,b,ca,q,ca,b,r]]=0, then find the value of (p)/(p-a)+(q)/(q-b)+(r)/(r-c)

Let a_r=r(.^7C_r),b_r=(7-r)(.^7C_r) and A_r=[(a_r,0),(0,b_r)] . If A=sum_(r=0)^7 A_r=[(a,0),(0,b)] , then find the value of a+b .

If a,b,c in R such that a^3+b^3+c^3=2 and |[a,b,c],[b,c,a],[c,a,b]|=0 then find abc

If P=[(x,0, 0),( 0,y,0 ),(0, 0,z)] and Q=[(a,0 ,0 ),(0,b,0 ),(0, 0,c)] , prove that P Q=[(x a,0 ,0 ),(0,y b,0),( 0 ,0,z c)]=Q P

If det[[p,b,ca,q,ca,b,r]]=0, find the value of (p)/(p-a)+(q)/(q-b)+(r)/(r-c),p!=a,q!=b,r!=c

If two events AandB are such that P(A^(c))=0.3,P(B)=0.4, and P(A nn B^(c))=0.5 ,then find the value of P[B/(A uu B^(c))]