Ex 3.4, 13

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Ex3.4, 13 Find the inverse of each of the matrices, if it exists.[■8(2&−3@−1&2)] Let A =[■8(2&−3@−1&2)] We know that A = IA [■8(2&−3@−1&2)]= [■8(1&0@0&1)] A R1 →R1 + R2 [■8(𝟐+(−𝟏)&−3+2@−1&2)]= [■8(1+0&0+1@0&1)] A [■8(𝟏&−1@−1&2)] = [■8(1&1@0&1)] A R2 →R2+ R1 [■8(1&−1@𝟏+(−𝟏)&2+(−1))] = [■8(1&1@0+1&1+1)] A [■8(1&−1@𝟎&1)] = [■8(1&1@1&2)] A R1 →R1 + R2 [■8(1+0&−𝟏+𝟏@0&1)] = [■8(1+1&1+2@1&2)] A [■8(1&𝟎@0&1)] = [■8(2&3@1&2)] A I= [■8(2&3@1&2)] A This is similar to I = A-1A Thus, A-1 =[■8(2&3@1&2)]