Question: Show that the block upper triangular matrix A in Example 5 is invertible if and only if both A 11 and A 22 are invertible.

Show that the block upper triangular matrix A in Example 5 is invertible if and only if both A₁₁and A₂₂ are invertible.

Data from in Example 5

EXAMPLE 5 A matrix of the form A = [ A11 A12

EXAMPLE 5 A matrix of the form A = [ A11 A12 0 A22 is said to be block upper triangular. Assume that A is px p, A22 is q xq, and A is invertible. Find a formula for A-1.

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