If B is a 3 × 3 matrix such that B 2 = 0 , then d e t .   I + B 50 - 50 B is equal to :

Question

If B is a 3 &#215; 3 matrix such that B 2 = 0 , then d e t . &#160; I + B 50 - 50 B is equal to :

Aicharya · Accepted Answer

B 2 = 0 &#8658; B 4 = B 6 = B 8 = . . . . = B 50 = 0 and B 3 = B 2 B = 0 B = 0 &#8658;&#160; I + B 50 = I + C 1 50 B (higher powers are zero) &#8756; d e t . I + B 50 - 50 B &#160; = d e t . &#160; I + 5 0 C 1 B - 5 0 B = d e t . I = 1

If B is a 3 &#215; 3 matrix such that B 2 = 0 , then d e t . &#160; I + B 50 - 50 B is equal to :

Solution

If B is a 3 × 3 matrix such that B 2 = 0 , then d e t . I + B 50 - 50 B is equal to :