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Shortcut method of finding inverse of a 2x2 matrix useful for students of diploma CET & engineering CET.

B.Sudhakar
31/12/2016 0 0

Instead of going through conventional method of finding inverse of a 2 x 2 matrix, let us solve following example using shortcut method that is useful for students taking CET exams where time is a constraint.

# only square matrix has inverse #

Find inverse of 2 x 2 matrix 'A' =  ⌈3  5 ⌉                                                                                                                                           ⌊1  2 ⌋

Now determinant | A | = { 3 x 2 - ( 5 x 1 )} = ( 6 - 5 ) = (1)

To find adjoint  A,  simply interchange elements ( a ¹¹ and a ²² ) and change the signs of elements ( a ¹² and a ²¹ ) 

Hence adjoint A = ⌈ 2   -5 ⌉                                                                                                                                         ⌊ -1   3 ⌋

 Finally A‾¹ = adj A / | A |

Ie:         A‾¹   =    ⌈ 2.   -5 ⌉  ÷ 1                                                                                                                                ⌊-1     3 ⌋

                      ⌈ 2/1  -5/1 ⌉                                                                                                 ∴   A‾¹  =           ⌊ -1/1   3/1 ⌋               

A‾¹  =   ⌈ 2   -5 ⌉                                                                                                                                         ⌊ -1   3 ⌋

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