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If A= [ array ll a & b b & a array ] and ( array ll A & I array )^2= [ array ll & & array ] where I is the identity matrix then

Options

  1. A=a^2+b^2, =2 a b
  2. B=a^2+b^2, =a^2-b^2
  3. C=2 a b, =a^2+b^2
  4. D=a^2+b^2, =a b

Correct answer

A. =a^2+b^2, =2 a b

Step-by-step solution

Given A = bmatrix a & b b & a bmatrix and I = bmatrix 1 & 0 0 & 1 bmatrix . The expression is given as A^2 = bmatrix & & bmatrix . Calculating A^2 : A^2 = bmatrix a & b b & a bmatrix bmatrix a & b b & a bmatrix = bmatrix a^2 + b^2 & ab + ba ba + ab & b^2 + a^2 bmatrix A^2 = bmatrix a^2 + b^2 & 2ab 2ab & a^2 + b^2 bmatrix Comparing this with bmatrix & & bmatrix , we get = a^2 + b^2 and = 2ab . Answer: =a^2+b^2, =2 a b

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