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Question

which of the following is true, if A is an invertible square matrix :-


A
(AT)1=(A1)T
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B
(AT)1=(A1)(AT)
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C
(AT)=(A1)T
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D
(AT)1=(AT)(A1)
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Solution

The correct option is A (AT)1=(A1)T
Since A is invertible matrix.(A|0(AT0             [(AT=(A|] AT is also invertible Now,A.A1=I=A1.A(A.A1)T=(I)T=(A1.A)T(by reversal law for transpose](A1)T(AT)=I=AT(A1)T (AT)1=(A1)T

Mathematics

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