IIT JEE Advanced 2009 Paper 1

We have
[

0	a	b
a	0	c
b	c	1

]
We can see that either b = 0 or c = 0 ⇒ |A| ≠ 0; therefore, two matrices.
[

0	a	b
a	1	c
b	c	0

]
Now, either a = 0 or c = 0 ⇒ |A| ≠ 0; therefore, two matrices
[

1	a	b
a	0	c
b	c	0

]
Now, either a = 0 or b = 0 ⇒ |A| ≠ 0; therefore, two matrices.
[

1	a	b
a	1	c
b	c	1

]
When a = b = 0 ⇒ A = 0.
When a = c = 0 ⇒ A = 0.
When b = c = 0 ⇒ A = 0.
Therefore, there are only six matrices.