Question

35. Prove: If A and B are n × n matrices, then tr(A + B) = tr(A) + tr(B) 36.

(a) Prove: If AB and BA are both defined, then AB and BA are square matrices.

(b) Prove: If A is an m × n matrix and A(BA)is defined, then B is an n × m matrix.​

Answer 1

Answer:

Step-by-step explanation:

Recall that two matrices can be multiplied only if the number of columns of the first matrix and the number of rows of the second matrix are equal.

In that case the size of the resulting matrix will be the number of rows of the first matrix times the number of columns of the second matrix.