Question

9. If B is a non-singular matrix and A is a square matrix, then der(B-¹AB) is equal to
(a) Det (A-¹)
(b) Det(B-¹)
(c) Det(A)
(d) Det(B)
​

Answer 1

Answer:

(c)

Step-by-step explanation:

det (B-1AB)

= det (B-1) . det (A) . det (B)

= (1/det (B)) . det (A) . det (B)

= det (A)  [proved]

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How det (B-1) = 1/det(B) ?

=> We know, BB-1 = I

So, det (BB-1) = det (I)

=> det (B) . det (B-1) = 1

=> det (B-1) = 1/det(B)