JEE Main20231 Feb 2023Evening ShiftMathematicsMatricesActual

If A = 1 2 1 3 - 3 1 then,

Options

AA 30 - A 25 = 2 I
BA 30 + A 25 + A = I
CA 30 + A 25 - A = I
DA 30 = A 25

Correct answer

C. A 30 + A 25 - A = I

Step-by-step solution

Given A = 1 2 1 3 - 3 1 A 2 = 1 4 1 3 - 3 1 1 3 - 3 1 = 1 4 1 - 3             2 3 - 2 3 - 3 + 1 A 2 = 1 2 - 1           3 - 3 - 1 A 3 = 1 4 - 1           3 - 3 - 1 - 1           3 - 3 - 1 ⇒ A 3 = 1 4 - 4           0 0 - 4 = - 1           0 0 1 ⇒ A 3 = - I   . . . . . ( 1 ) Now from equation 1 , A 30 = ( - I ) 10 = I   . . . . . ( 2 ) Again f

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