In R there is a problem of intercept and without intercept ,Pearson's Correlation does not follow! Why? (see the bolded resuls)

Question

Xvec <- rnorm(200)
Yvec <- 2.6*Xvec + rnorm(200)

lmodxy <- lm(Xvec ~ Yvec)
lmodyx <- lm(Yvec ~ Xvec)
summary(lmodxy)

Output

Call:
lm(formula = Xvec ~ Yvec)
Residuals:
 Min       1Q   Median       3Q      Max
-0.85820 -0.24244  0.01888  0.23892  0.75319
Coefficients:
            Estimate Std. Error t value Pr(>|t|)

(Intercept) 0.015986   0.023954   0.667    0.505

Yvec        0.336546   0.009412  35.758   <2e-16 ***

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Residual standard error: 0.3379 on 198 degrees of freedom
Multiple R-squared:  0.8659,    Adjusted R-squared:  0.8652 
F-statistic:  1279 on 1 and 198 DF,  p-value: < 2.2e-16

Code

lmodxy$coefficients[2]*lmodyx$coefficients[2]
# Yvec: 0.865911394725732
cor(Yvec,Xvec)^2
0.865911394725732
lmodxy2 <- lm(Xvec ~ Yvec-1)
lmodyx2 <- lm(Yvec ~ Xvec-1)
summary(lmodxy2)

Output

 Call:
lm(formula = Xvec ~ Yvec - 1)
Residuals:
     Min       1Q   Median       3Q      Max 
-0.84247 -0.22664  0.03424  0.25282  0.76821
Coefficients:
     Estimate Std. Error t value Pr(>|t|)

Yvec 0.336094   0.009374   35.85   <2e-16 ***

Signif. codes:  0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.3374 on 199 degrees of freedom
Multiple R-squared:  0.8659,    Adjusted R-squared:  0.8653 
F-statistic:  1285 on 1 and 199 DF,  p-value: < 2.2e-16

Code

lmodxy2$coefficients[1]*lmodyx2$coefficients[1]
#  Yvec: 0.865940634163253

Why the correlation squared is not the same as the product of slopes without intercepts whereas it is the same in the case of products with intercepts

it should be -------- Y_hat = bX + a and X_hat = BY + A then Cor(Y,X)^2 = (b*)(B*)