A block matrix has the form

In which A, B, C, D are matrices with respective sizes i × k,i × l, j × k, j × l.
(a) What is the size of M?
(b) Write out the block matrix M when

(c) Show that if

is a block matrix whose blocks have the same size as those of M, then

i.e., matrix addition can be done in blocks.
(d) Show that if

has blocks of I compatible size, the matrix product is

Explain what "compatible" means.
(e) Write down a compatible block matrix P for the matrix M in part (b). Then validate the block matrix product identity for your chosen matrices.

M= C D 11 301 10 121 BD )) 1-21 3 9)