Using the property of determinants and without expanding, prove that:`|2 7 65 3 8 75 4 9 86|=0`

Using the property of determinants and without expanding, prove that: |[2, 7, 65],[ 3 ,8 ,75 ],[4, 9,86]|=0

Using the property of determinants and without expanding, prove that |(2,7,65), (3,8,75), (5,9,86)|=0

Using the property of determinants and without expanding, prove that: |0a-b-a0-c b c0|=0

Using the property of determinants and without expanding, prove that: |-a^2a b a c b a b^2b cc a c b-c^2|=4a^2b^2c^2

Using the property of determinants and without expanding, prove that: |[-a^2,a b, a c],[ b a, -b^2,b c],[c a, c b,-c^2]|=4a^2b^2c^2

Using the property of determinants and without expanding, prove that: |b+c q+r y+z c+a r+p z+x a+b p+q x+y|=2|a p x b q y c r z|

Using the property of determinants and without expanding, prove that: |[x, a ,x+a],[ y, b, y+b],[ z, c, z+c]|=0

Using the property of determinants and without expanding, prove that: |1b c a(b+c)1c a b(c+a)1a b x(a+b)|=0

Using the property of determinants and without expanding, prove that: |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b, c(a+b)]|=0

Using the property of determinants and without expanding, prove that: |[b+c, q+r, y+z],[ c+a, r+p, z+x],[ a+b, p+q, x+y]|=2|[a, p, x],[ b, q ,y],[ c, r, z]|