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

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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.

 

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