IN Gate 2007 - Matrix

Question

Let A be an nxn real matrix such that A^2=I and y be an n-dimensional vector. Then the linear system of equations AX=Y has

A) No solution

B) Unique Solution

C) More than one but finitely many independent solutions

D) infinitely many independent solutions

Comments

I didn`t get your solution but Determinant of $A \ is \neq0$ how it implies that when you will create augument matrix $AY$ it will result the same rank which will be equal to no of unknowns?

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If |A| ≠0 then rank of A = n. Since X is a vector of n dimension so I took the no. Of unknowns as n. As it equal to the rank so unique solution exists.

If I am wrong then please correct it and also say how to solve it.

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@MiNiPanda, U r right. since |A| ≠0 so rank of (A|Y) = rank of (A) , Y is a n-dimensional vector. hence unique solution exist only.

Answer 1

take A=identity matrix you will get a unique solution for any y. simple!