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Question

Let A be a square matrix of order 3 such that A = 11 and B be the matrix of confactors of elements of A. Then, B2 = ________________.

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Solution

Given:
A be a square matrix of order 3
A = 11
B be the matrix of cofactors of elements of A

Since, B be the matrix of cofactors of elements of A
B=adj ATB=adj ATB=adj A AT=AB2=adj A2

As we know,
adj A=An-1, where n is the order of AB=An-1B=A3-1 Order of A is 3B=A2 B=112 A=11B=121B2=1212B2=14641


Hence, B2 = 14641.

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