Q6 of 29 Page 1

Given A = compute A–1 and show that 2 A–1 = 9I – A.

A =


|A| = 2 × 7 -  (-3) × (-4) = 14 – 12 = 2.

We will calculate the co factors of the matrix A,

∴  A11 = 7, A12 = 4, A21 = 3, A22 = 2


adj(A) = = =


Now,

To Prove: 2 A–1 = 9I – A

Proof: 


and, 



L.H.S = R.H.S

Hence, Proved.

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