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Question
Find the adjoint of the following matrix.
`[(2,-3),(3,5)]`
Solution
Let A = `[(2,-3),(3,5)]`
Here, a11 = 2, M11 = 5
∴ A11 = (− 1)1+1(5) = 5
a12 = − 3, M12 = 3
∴ A12 = (− 1)1+2(3) = − 3
a21 = 3, M21 = − 3
∴ A21 = (− 1)2+1(− 3) = 3
a22 = 5, M22 = 2
∴ A22 = (− 1)2+2 = 2
∴ the co-factor matrix = `[("A"_11,"A"_12),("A"_21,"A"_22)]`
= `[(5,-3),(3,2)]`
∴ adj A = `[(5,3),(-3,2)]`
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