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If A is an invertible matrix, then what is det (A-1) equal to?

If A is an invertible matrix, then what is det (A-1) equal to? Correct Answer <span class="math-tex">\(\frac{1}{{\det A}}\)</span>

Concept:

The determinant of the inverse of an invertible matrix is the inverse of the determinant:

i.e., det(A-1) = 1 / det(A)

Calculation:

Here, A is an invertible matrix, 

As we know, AA-1 = I

Taking determinants both sides, we get

⇒ det (AA-1) = det I

⇒ det(A-1) × det (A) = 1             

∴ det(A-1) = 1/ det (A)

Hence, option (2) is correct.

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