Q20 of 256 Page 7

Write the value of .

Let

Expanding along R₁,

we get ∆= sin20°cos70°-(-cos20°)sin70°

= sin20°cos70°+cos20°sin70°

Since sin(A+B)= sinAcosB+cosAsinB

Hence, sin20°cos70°+cos20°sin70°=sin(20°+70°)

=sin(90°)

Hence, ∆=1

Let A = [a_ij] be a square matrix of order 3 × 3 and C_ij denote cofactor of a_ij in A. If |A| = 5, write the value of a₃₁C₃₁ + a₃₂C₃₂ + a₃₃C₃₃.

In question 18, write the value of a₁₁C₂₁ + a₁₂C₂₂ + a₁₃C₂₃.

If A is a square matrix satisfying A^TA = I, write the value of |A|.

If A and B are square matrices of the same order such that |A| = 3 and AB = I, then write the value of |B|.