Suppose A is any 3 3 non-singular matrix and (A-3 I)(A-5 I)=O , where I=I₃ and O=O₃ . If A+ A⁻¹=4 I , then + is equal to

Step-by-step solution

We have aligned &(A-3 I)(A-5 I)=O & A^2-8 A+15 I=O aligned Multiplying both sides by A⁻¹ , we get; aligned A⁻¹ A A-8 A⁻¹ A+15 A⁻¹ I=A⁻¹ O & A-8 I+15 A⁻¹=O & A+15 A⁻¹=8 I & A 2 + 15 A⁻¹ 2 =4 I & + = 1 2 + 15 2 = 16 2 =8 aligned