Question

7) A has 'a' rows and 'a +3 columns. B has 'brows and '17-b' columns and if
both products AB and BA exist, find a, b?

please tell the answer​

Answer 1

Assuming that you are talking under the context of matrices

Given,

The matrix A of (a) rows and (a+3) columns is denoted by

The matrix B is denoted by (b) rows and (b-17)  

Given that $A\times B$ exists, implies that the number of columns of A must equal the number of rows of B

$\\\implies a+3=b\\\implies a-b=3\:---\:(eqtn.\:1)$

Also, given that $B\times A$ exists, implies that the number of columns of B must equal the number of rows of A

$\\\implies 17-b=a\\\implies a+b=17\:---\:(eqtn.\:2)$

Adding equation 1 and 2, we get

$(a-b)+(a+b)=17+3\\\implies 2a=20\\\implies a = 10$

Substituting value of a in equation 2, we get

$10+b=17\\\implies b=17-10\\\implies b = 7$

∴ a = 10 and b = 7