Let A and B be two 3×3 real matrices such that A^2-B^2 is invertible matrix. If A^5=B^5 and A^3 B^2=A^2 B^3, then the value of the determinant of the…

Question

Let A and B be two 3×3 real matrices such that A^2-B^2 is invertible matrix. If A^5=B^5 and A^3 B^2=A^2 B^3, then the value of the determinant of the matrix A^3+B^3 is equal to :

MARKS Content Team · Accepted Answer

Correct answer: (D) 0. Let C=A^2-B^2;C≠0 and A^5=B^5 ...1 A^3 B^2=A^2 B^3 ...2 Subtracting equation 2 from 1, we get A^5-A^3B^2=B^5-A^2B^3 ⇒A^3 A^2-B^2+B^3 A^2-B^2=O Post multiplying inverse of A^2-B^2: A^3+B^3=O⇒A^3+B^3=0

Let $A$ and $B$ be two $3 \times 3$ real matrices such that $(A^{2} - B^{2})$ is invertible matrix. If $A^{5} = B^{5}$ and $A^{3} B^{2} = A^{2} B^{3},$ then the value of the determinant of the matrix $A^{3} + B^{3}$ is equal to :

Solution

Relevant Questions

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

Solution

Relevant Questions

Let $A$ and $B$ be two $3 \times 3$ real matrices such that $(A^{2} - B^{2})$ is invertible matrix. If $A^{5} = B^{5}$ and $A^{3} B^{2} = A^{2} B^{3},$ then the value of the determinant of the matrix $A^{3} + B^{3}$ is equal to :