The value of `|(a^(2),-ab,-ac),(-ab,b^(2),-bc),(ca,bc,-c^(2))|`, is

What is |{:(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2)):}| equal to ?

The value of |(a,a^(2) - bc,1),(b,b^(2) - ca,1),(c,c^(2) - ab,1)| , is

If a,b, c, lambda in N , then the least possible value of |(a^(2)+lambda, ab,ac),(ba,b^(2)+lambda,bc),(ca, cb, c^(2)+lambda)| is

Using properties of determinant prove that |(a^(2)+1, ab, ac),(ab, b^(2)+1, bc),(ca, cb,c^(2)+1)|=(1+a^(2)+b^(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)=

Consider the function f(x) = |{:(a^(2)+x,,ab,,ac),(ab,,b^(2)+x,,bc),(ac,,bc,,c^(2)+x):}| In which of the following interval f(x) is strictly increasing

Prove the following by multiplication of determinants and power cofactor formula |{:(0,c,b),(c,0,a),(b,a,0):}|^(2)=|{:(b^(2)+v^(2),ab,ac),(ab,c^(2)+a^(2),bc),(ac,bc,a^(2)+b^(2)):}| =|{:(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2)):}|=4a^(2)b^(2)c^(2)

Using properties of determinant, if |(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)| = mua^2b^2c^2 , find mu

The determinant Delta=|{:(,a^(2)(1+x),ab,ac),(,ab,b^(2)(1+x),(bc)),(,ac,bc,c^(2)(1+x)):}| is divisible by