How to select randomly rows and columns in each row in a list in R?

I have a list in which there is a 5x5 matrix data set. I want to randomly select 2 rows and within each row I want to select 3 elements not necessarily from same columns.

So, I generated three data sets and made a list. I was able to select 2 rows randomly but have a difficulty in selecting 3 elements randomly not selecting columns.

Here is my code.

    ### Generate three data sets
    dat1 <- (matrix(rnorm(25), ncol=5))
    dat2 <- (matrix(rnorm(25), ncol=5))
    dat3 <- (matrix(rnorm(25), ncol=5))

    all.dat <- list(dat1=dat1, dat2=dat2, dat3=dat3)
    all.dat

    #$`dat1`
    #           [,1]      [,2]       [,3]        [,4]       [,5]
    #[1,]  1.4394742 0.7064418 -1.3472468  0.52847179 -0.7642337
    #[2,]  0.2490570 0.7510308 -0.7028238 -0.09730666 -0.6340773
    #[3,]  0.8981850 0.7592610  0.9139721 -0.45700647 -0.2727481
    #[4,] -1.0467119 0.2147032 -3.2104254 -0.17797056  0.8897180
    #[5,] -0.5437118 0.5803862 -0.1814992  1.93316139 -1.3708932

    #$dat2
    #          [,1]       [,2]          [,3]         [,4]       [,5]
    #[1,] 1.0442187 -1.4156893  0.5606035101 -1.350030718  0.1538721
    #[2,] 0.2080905 -1.7748005  0.8620324724 -0.169071336 -1.7537700
    #[3,] 0.9153835 -0.9884572 -1.7279901136 -1.334516414  0.5773021
    #[4,] 0.1359423 -1.5107088 -1.4289650078 -0.002001498 -0.4712699
    #[5,] 0.1695023 -0.7315209 -0.0003996577 -1.043326258  1.2939485

    #$dat3
    #           [,1]        [,2]         [,3]       [,4]       [,5]
    #[1,] -1.4994878 -0.59179084  0.998017255  1.4021344  0.5929842
    #[2,]  0.3424003  1.33568858  2.214968765 -0.2434351  1.3588000
    #[3,] -1.0117892  0.91065720 -0.761932994 -0.8117838 -0.4094731
    #[4,] -0.1694781 -0.02937177 -0.826337270  0.2178774 -0.6427046
    #[5,]  0.3413101 -0.56911900  0.001363063  0.5579126 -0.9373204

    ### Select rows and columns.
    all.dat.sel.1 <- 
    lapply(all.dat, function(x) {
    x[sample(nrow(x), size = 2), sample(ncol(x), size = 3)]
    })

    all.dat.sel.1

    #$`dat1`
    #           [,1]       [,2]       [,3]
    #[1,] -0.4570065  0.8981850 -0.2727481
    #[2,]  1.9331614 -0.5437118 -1.3708932

    #$dat2
    #              [,1]         [,2]       [,3]
    #[1,] -0.0003996577 -1.043326258  1.2939485
    #[2,] -1.4289650078 -0.002001498 -0.4712699

    #$dat3
    #           [,1]      [,2]       [,3]
    #[1,] -1.4994878 1.4021344  0.9980173
    #[2,] -0.1694781 0.2178774 -0.8263373

Then, I was able to select rows randomly but elements in each row were from the same columns. For example, values, -1.4994878 in row 1 and -0.1694781 in row 2 were from column 1 in dat3.

What I would like to have is something like this:

    #$dat3
    #           [,1]        [,2]         [,3]
    #[1,] -1.4994878 0.998017255    0.5929842
    #[4,]  0.2178774 -0.02937177 -0.826337270

There is an example of this (https://stackoverflow.com/questions/53095050/sample-random-column-for-each-row-in-data-frame). However, it applied to data frame not list data.