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 :
Solution
Let $A = \left[ {\matrix{
a & b \cr
b & c \cr
} } \right]$<br><br>$${A^2} = \left[ {\matrix{
a & b \cr
b & c \cr
} } \right]\left[ {\matrix{
a & b \cr
b & c \cr
} } \right] = \left[ {\matrix{
{{a^2} + {b^2}} & {ab + bc} \cr
{ab + bc} & {{c^2} + {b^2}} \cr
} } \right]$$<br><br>$= {a^2} + 2{b^2} + {c^2} = 1$<br><br>$a = 1,b = 0,c = 0$<br><br>$a = 0,b = 0,c = 1$<br><br>$a = - 1,b = 0,c = 0$<br><br>$c = - 1,b = 0,a = 0$
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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