Q25 of 37 Page 293

If A = show that A-1= A’.

We have,

To show: A-1 = A’


Firstly, we find the Transpose of A, i.e. A.’



Here,


So, …(i)


Now, we have to find A-1 and


Calculating |A|


Expanding |A| along C1, we get










= -1


Now, we have to find adj A, and for that, we have to find co-factors:














= A’ [from eq. (i)]


Thus, A-1 = A’


Hence Proved


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