Still breathing after this morning huh ?
As is a liner transformations there exists and matrix such that to find this matrix you need to find the images of the vectors and under . This all lies down the understanding how matrix multiplication works.
I do this row by row, you see that the vector is preserved under the transformation, so the first row is one combined linearly with no j's or k's
so the first row is
for the next row you combining one with one and no k's
so we have
Then similarly for the next row your combining 1 i with 1 k.
to check this is correct just multiple the two.
so is given by