Repeat

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

Repeat

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

Given

A = [\begin{array}{ccc} a^{2} & a m p; a b & a m p; a c \\ a b & a m p; b^{2} & a m p; b c \\ a c & a m p; b c & a m p; c^{2} \end{array}]

A^{2}, = A \times, A = [\begin{array}{ccc} a^{2} & a m p; a b & a m p; a c \\ a b & a m p; b^{2} & a m p; b c \\ a c & a m p; b c & a m p; c^{2} \end{array}] [\begin{array}{ccc} a^{2} & a m p; a b & a m p; a c \\ a b & a m p; b^{2} & a m p; b c \\ a c & a m p; b c & a m p; c^{2} \end{array}]

= [\begin{array}{ccc} a^{4} + a^{2} b^{2} + a^{2} c^{2} & a m p; a^{3} b + a b^{3} + a b c^{2} & a m p; a^{3} c + a b^{2} c + a c^{3} \\ a^{3} b + a b^{3} + a b c^{2} & a m p; a^{2} b^{2} + b^{4} + b^{2} c^{2} & a m p; a^{2} b c + b^{3} c + b c^{3} \\ a^{3} c + a b^{2} c + a c^{3} & a m p; a^{2} b c + b^{3} c + b c^{3} & a m p; a^{2} c^{2} + b^{2} c^{2} + c^{4} \end{array}]

= [\begin{array}{ccc} a^{2} (a^{2} + b^{2} + c^{2}) & a m p; a b (a^{2} + b^{2} + c^{2}) & a m p; a c (a^{2} + b^{2} + c^{3}) \\ a b (a^{2} + b^{2} + c^{2}) & a m p; b^{2} (a^{2} + b^{2} + c^{2}) & a m p; b c (a^{2} + b^{2} + c^{2}) \\ a c (a^{2} + b^{2} + c^{2}) & a m p; b c (a^{2} + b^{2} + c^{2}) & a m p; c^{2} [a^{2} + b^{2} + c^{2}] \end{array}]

since

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

= [\begin{array}{ccc} a^{2} & a m p; a b & a m p; a c \\ a b & a m p; b^{2} & a m p; b c \\ a c & a m p; b c & a m p; c^{2} \end{array}] = A

⟹ A^{2} = A

Please subscribe our Youtube channel to unlock this solution.