Matrix A is non-singular matrix and (A-3 I)(A-5 I)=0, then 15/8 A^{-1}= ..

Correct Answer is : I−18A{I}-1/8 AI−81A

Correct Answer is : I−18A{I}-1/8 AI−81A

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MHTCET 26 Apr 2025 Shift 1 Paper

Question : 143 of 150

Marks: +1, -0

(A-3 I)(A-5 I)=0

\frac{15}{8} A^{-1}=\ldots .

Solution:

Concept:

Expand the given matrix equation and multiply by

A^{-1}

to isolate

\frac{15}{8}A^{-1}

Explanation:

Given:

(A-3I)(A-5I)=0

Expanding the product:

A^2 - 5A - 3A + 15I = 0

A^2 - 8A + 15I = 0

Since

A

is non-singular, multiply both sides on the right by

A^{-1}

A^2 A^{-1} - 8A A^{-1} + 15I A^{-1} = 0

A - 8I + 15A^{-1} = 0

Rearrange:

15A^{-1} = 8I - A

Dividing both sides by 8:

\frac{15}{8}A^{-1} = I - \frac{1}{8}A

Answer:

\frac{15}{8}A^{-1} = I - \frac{1}{8}A

Hence, the correct option is C.

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