"a student is randomly choosing the answer to each of five true-false questions in a test. how many possible ways can the student answer the five questions? "

..........

Gosh, that's just the list of binary numbers he can write with five bits.

It's 32 .

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b