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p-values of correlation matrix

Have a look at function rcor.test() from package ltm, e.g.,

library(ltm)
mat <- matrix(rnorm(1000), 100, 10, dimnames = list(NULL, LETTERS[1:10]))
rcor.test(mat)
rcor.test(mat, method = "kendall")
rcor.test(mat, method = "spearman")


I hope it helps.

Best,
Dimitris