The matrix A has x rows and x 5 columns The matrix B has y r...........

Mathematics (NDA) Matrices and Determinants

The matrix A has x rows and x + 5 columns. The matrix B has y rows and 11 − y columns. Both AB and BA exist. What are the values of x and y respectively?

8 and 3

3 and 4

3 and 8

8 and 8

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Explanation:

For existence of both matrices, number
of rows of matrix A = number of
columns of matrix B and number of rows
of matrix B = number of columns of
matrix A
i.e., x = 11- y
and y =x + 5
Solving above equations, we get
x = 8 and y = 3.