Let A and B be 10 × 10 matrices that are partitioned into submatrices as follows:

(a) If A11 is a 6 × 5 matrix, and B11 is a k × r matrix, what conditions, if any, must k and r satisfy in order to make the block multiplication of A times B possible?
(b) Assuming the block multiplication is possible, how would the (2, 2) block of the product be determined?

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An A12 -1A21 A22 B B12 =1 B21 B22