#### Provide solution for rd sharma maths class 12 chapter adjoint and inverse of a matrix exercise multiple choice question question 12

option (d)$\lambda \neq 0$

Given: A satisfies the equation $x^{3}-5x^{2}+4x+ \lambda =0$

Hint: since A satisfies the equation so put  x = A

Solution :

Since A satisfies the equation ∴ $A^{3}-5A^{2}+4A+ \lambda =0$

A-1 Exist if $\lambda \neq 0$

since if $\lambda =0$ then the above equation gives A = 0 and in that case A-1  will not exist

Hence option (d) is correct.