QJEEM21Ma060b: JEE Main 2021 Mathematics - Class 12 JEEM21Ma060b Solution: Let A be a symmetric matrix of order 2 with integer entries. If …

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QJEEM21Ma060b: JEE Main 2021 Mathematics - Class 12 JEEM21Ma060b Solution: Let A be a symmetric matrix of order 2 with integer entries. If …

Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A² is 1, then the possible number of such matrices is :

Multiple Choice Options

A 6
B 4
C 1
D 12

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Accepted Answer

Let

A = [\begin{matrix} a & b \\ b & c \end{matrix}]

A^{2} = [\begin{matrix} a & b \\ b & c \end{matrix}] [\begin{matrix} a & b \\ b & c \end{matrix}] = [\begin{matrix} a^{2} + b^{2} & a b + b c \\ a b + b c & c^{2} + b^{2} \end{matrix}]

= a^{2} + 2 b^{2} + c^{2} = 1

a = 1, b = 0, c = 0

a = 0, b = 0, c = 1

a = - 1, b = 0, c = 0

c = - 1, b = 0, a = 0

QJEEM21Ma060b: JEE Main 2021 Mathematics - Class 12 JEEM21Ma060b Solution: Let A be a symmetric matrix of order 2 with integer entries. If …

Multiple Choice Options

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