Let M be a 3 × 3 matrix with real entries. If MT M=I3, where I3 is a 3 × 3 identity matrix, then find the value of det. (M2-I3).

Question

Let M be a 3 × 3 matrix with real entries. If MT M=I3, where I3 is a 3 × 3 identity matrix, then find the value of det. (M2-I3). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

det. (M M-M prime M)= det. (M-M prime) ⋅ det. M ∵ M is 3 text rd order matrix ⇒ M-M prime is skew-symmetric matrix ⇒ det(M-M prime)=0

Q. Let $M$ be a $3 \times 3$ matrix with real entries. If $M^{T} M = I_{3}$ , where $I_{3}$ is a $3 \times 3$ identity matrix, then find the value of det. $(M^{2} - I_{3})$ .