Q23 of 37 Page 293

If A = , show that A-1 = A2.

We have,

To show: A-1 = A2


Firstly, we have to find A-1 and


Calculating |A|


Expanding |A| along C1, we get




= 1(0) – 2(0) + 1(0 – (-1))


= 1(1)


= 1


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












…(i)


Calculating A2





= A-1 [from eq. (i)]


Thus, A2 = A-1


Hence Proved


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