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Step 1 Given that, A,B are symmetric matrices. Prove that (BA−1)T(A−1BT)−1=I Step 2 Consider the LHS, (BA−1)T(A−1BT)−1=(A−1)T(B)T(BT)−1(A−1)−1 =(A−1)TIA [∵(BT)(BT)−1=I and (A−1)−1=A] =(A−1)TAT [∵A=AT] =(AT)−1AT [∵(AT)−1=(A−1)T] =I [∵(AT)(AT)−1=I] =RHS Hence , the required is obtained.
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