JEE Main202622 January 2026Morning ShiftMathematicsMatricesActual

If A = [ array ll 2 & 3 3 & 5 array ] , then the determinant of the matrix ( A ²⁰²⁵-3 ~A ²⁰²⁴+ A ²⁰²³ ) is

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Correct answer

D. 16

Step-by-step solution

A = bmatrix 2 & 3 3 & 5 bmatrix A^2 = bmatrix 13 & 21 21 & 34 bmatrix |A²⁰²⁵ - 3A²⁰²⁴ + A²⁰²³| = | A²⁰²³ ( A^2 - 3A + I ) | = |A|²⁰²³ |A^2 - 3A + I| = 1 vmatrix 8 & 12 12 & 20 vmatrix = 160 - 144 = 16

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