If ( A= [ array cc 2 & - 2 2 & 2 array ] ) and ( A+A^ T =I ), where ( I ) is the unit matrix of ( 2 2 & ~A ^ T ) is the transpose of ( A ), then the value of ( ) is equal to

Step-by-step solution

Given that, A = [ array cc 2 & - 2 2 & 2 array ] So, A ^ T = [ array cc 2 & 2 - 2 & 2 array ] Now, A + A ^ T = [ array ccc 2 2 & 0 0 & 2 2 array ]=2 2 [ array cc 1 & 0 0 & 1 array ] Given that, A + A ^ T = I so (2 2 ) I=I 2 2 =1 2 = 1 2 2 = 3 = 6