Assertion (A) : If `A=({:(cos alpha,sin alpha),(cos alpha,sin alpha):})and B=({:(cos alpha,cos alpha),(sin alpha,sin alpha):}),"then AB" ne 1`.
Reason (R) : The product of two matrices can never be equal to an identity matrix.

Options

A. Both A and R are individually true and R is the correct explanation of A
B. Both A and R are individually true but R is not the correct explanation of A
C. A is true but R is false
D. A is false but R is true

Answer

C

Explanation

`A=({:(cos alpha,sin alpha),(cos alpha,sin alpha):})`
`B=({:(cos alpha,sin alpha),(cos alpha,sin alpha):})`
`AB=({:(cos alpha,sin alpha),(cos alpha,sin alpha):})({:(cos alpha,cos alpha),(sin alpha,sin alpha):})`
`({:(cos^(2)alpha+sin^(2)alpha,cos^(2)alpha+sin^(2)alpha),(cos^(2)alpha+sin^(2)alpha,cos^(2)alpha+sin^(2)alpha):})`
`=({:(1,1),(1,1):})ne I`,
So, A is true. Since product of two matrix may be equal to identity matrix.
so, R is false and A is true.