Let A and B be two 3 [] 3 real matrices such that (A2 - B2) is invertible matrix.

Question

Let A and B be two 3 $$\times$$ 3 real matrices such that (A2 - B2) is invertible matrix. If A5 = B5 and A3B2 = A2B3, then the value of the determinant of the matrix A3 + B3 is equal to :

Accepted Answer

C = A2 - B2;, C, $$\ne$$ 0

A2 = B5 and A3B2 = A2B2

Now, A5 - A3B2 = B5 - A2B3

$$\Rightarrow$$ A3 (A2 - B2) + B3 (A2 - B2) = 0

$$\Rightarrow$$ (A3 + B3(A2 - B2) = 0

$$ \Rightarrow $$ A3 + B3 = 0 $$\left( \because{\left| {{A^2} - {B^2} \ne 0} \right|} \right)$$

Solutions · 1