Problem
1 السؤوال If is $\lambda$ an eigenvalue of non-singular matrix $A$ then the eigenvalue of $A^{-1}$ is $\lambda \bigcirc$ $-\frac{1}{\lambda} \bigcirc$ $-\lambda \bigcirc$ $\frac{1}{\lambda} \bigcirc$ सhyl iks 2 تय, 3
Solution
Step 1 ：Given a non-singular matrix A with eigenvalue \(\lambda\), we have the equation Ax = \(\lambda\)x
Step 2 ：Multiply both sides by A⁻¹: A⁻¹Ax = A⁻¹\(\lambda\)x
Step 3 ：Simplify: x = \(\frac{1}{\lambda}\)A⁻¹x
Step 4 ：The eigenvalue of A⁻¹ is \(\boxed{\frac{1}{\lambda}}\)
