Question

2 3
7. If A=
1 - 2 3
- 4 4 2 5
B = 4 5
and
2 1
then
1) AB, BA exist and equal
2) AB, BA exist and are not equal
3) AB exist and BA does not exist
4) AB does not exist and BA exist​

Answer 1

Here, A is a 2×2 matrix and B is a 2×3 matrix.

Clearly, the number of column in A =number of rows in B.

∴ AB exists and it is a 2×3 matrix.

AB=[5243][365814]

=[5.3+4.62.3+3.65.5+4.82.5+3.85.1+4.42.1+3.4]

=[15+246+1825+3210+245+162+12]=[392457342114].

Again, B is a 2×3 matrix and A is a 2×2 matrix.

∴ number of columns in B≠ number of rows in A.

So, BA does not exist.