Solve the equation

Solve:

Prove that:

If x, y, z are different and

Prove that:

where p is any scalar.

If 
show that
a + b + c = abc(ab + bc + ca) where a , b , c are all different.

Let the three digit numbers A28,3B9 and 62C where A, B, and C are any integers between 0 and 9, be divisible by a fixed integer k. Show that the determinant

is divisible by k.

Prove that:

129.

Prove that:

Let A be a square matrix of order 3 × 3, then | kA | is equal to 

• k | A |
• k² | A |
• k ³| A |
• k ³| A |