Consider a 2 × 2 matrix \(M = \left[ {\begin{array}{*{20}{c}} {{v_1}}&{{v_2}} \end{array}} \right]\), where, v1 and v2 are the column vectors. Suppose \({M^{ - 1}} = \left[ {\begin{array}{*{20}{c}} {u_1^T}\\ {u_2^T} \end{array}} \right]\), where uT1 and uT2 are the row vectors. Consider the following statements.
Statement: uT1v1 = 1 and uT2v2 = 1
Statement: uT1v2 = 0 and uT2v1 = 0
Which of the following options is correct?1
Statement 1 is true and statement 2 is false
2
Statement 2 is true and statement 1 is false
3
Both the statements are true
4
Both the statements are false