If P = 3 2 1 2 - 1 2 3 2 ,   A = 1 1 0 1 and Q = P A P T , then P T   Q 2015   P is :

Question

If P = 3 2 1 2 - 1 2 3 2 , &#160; A = 1 1 0 1 and Q = P A P T , then P T &#160; Q 2015 &#160; P is :

Aicharya · Accepted Answer

P = 3 2 1 2 - 1 2 3 2 &#160; &#160; &#160; P T = 3 2 - 1 2 1 2 3 2 P P T = P T P = I Q 2015 = P A P T &#160; P A P T ......( 2015 terms) = P A 2015 &#160; P T ... i &#8756;&#160;&#160; P T &#160; Q 2015 &#160; P = P T P &#160; A 2015 P T P = A 2015 from.. i Given A = 1 1 0 1 &#8658; A 2 = 1 1 0 1 &#160; &#160; 1 1 0 1 = 1 2 0 1 &#8658; A 3 = 1 2 0 1 &#160; 1 1 0 1 = 1 3 0 1 &#8756; A 2015 = 1 2015 0 1

If P = 3 2 1 2 - 1 2 3 2 , &#160; A = 1 1 0 1 and Q = P A P T , then P T &#160; Q 2015 &#160; P is :

Solution

If P = 3 2 1 2 - 1 2 3 2 , A = 1 1 0 1 and Q = P A P T , then P T Q 2015 P is :