Loading [MathJax]/jax/output/SVG/jax.js
 
+0  
 
0
579
1
avatar

 

Find all 2×2 matrices ​A that have the property that for any 2×2  matrix B,


AB=BA.

 Mar 13, 2019
 #1
avatar+6251 
+1

A=ai,j, B=bi,jABBA=(a1,2b2,1a2,1b1,2(a1,1a2,2)b1,2+a1,2(b2,2b1,1)(a2,2a1,1)b2,1+a2,1(b1,1b2,2)a2,1b1,2a1,2b2,1)=0

 

From the first row we see a1,2=a2,1=0Then from row 2, a1,1=a2,2This agrees with row 3, and row 4 agrees with row 1 A=λI2,2, λC

.
 Mar 13, 2019
edited by Rom  Mar 13, 2019

2 Online Users

avatar
avatar