If `bc+ qr= ca+rp = ab+ pq =-1` then prove that
`|{:(ap,,a,,p),(bq,,b,,q),(cr,,c,,r):}|=0`

Prove that {:|(1+a,1,1),(1,1+b,1),(1,1,1+c)|=abc+bc+ca+ab

Evaluate Delta = {:|(1,a,bc),( 1,b,ca),(1,c,ab)|:}

Evaluate Delta -|(1,a,bc),(1,b,ca),(1,c,ab)|

The value of |(1,1,1),(bc,ca,ab),(b+c,c+a,a+b)|

The value of |(p,0,0,0),(a,q,0,0),(b,c,r,0),(d,e,f,s)| is :

Prove that {:[(1,ab,a+b),(1,bc,b+c),(1,ca,c+a):}]=(a-b)(b-c)(c-a)

Prove that |(1,a^2,bc),(a,b^2,ca),(1,c^2,ab)|=(a-b)(b-c)(c-a)

Prove that |(1,1,1),(bc,ca,ab),(b+c, c+a, a+b)| = (a-b)(b-c)(c-a)

Using the property of determinants prove that {:|( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) |:} = 3( a+b+c) ( ab+bc+ca)