Q1 of 39 Page 1

If A is an 3 x 3 invertible matrix, then what will be the value of k if det ( a^-1 ) = (deta )^k

[If A and B are square matrices of the same order, then det(AB) = det(A)det(B)]


∴ det(A × A−1) = det(A) × det(A−1)


⇒ det(I) = det(A) × det(A−1) = 1


∴ det(A−1) = (det(A))-1


∴ k = -1


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